Abstract Algebra 1 Basic Group Proof 3

>> DOWNLOAD LINK 🎞️ #1 <<

>> DOWNLOAD LINK 🎞️ #2 <<

>> COPY / PASTE LINK PLEASE 🎵 MP3 <<

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=jxJO0SB0Ffg

Let G be a finite group of even order. Show that G has an element a (not equal to the identity) such that a^2=e.","styleRuns":[{"startIndex":0,"length":113,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":113,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CMkBELsvGAIiEwi1ori1w-6LAxXgg_QHHeQnBgg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC2p4Sk8wU0IwRmZnGAYyJSIRIgtqeEpPMFNCMEZmZzAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CMkBELsvGAIiEwi1ori1w-6LAxXgg_QHHeQnBgg=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CMgBELovIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"6Rhg9LTHfXk","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/6Rhg9LTHfXk/hqdefault.jpg?sqp=-oaymwE8CKgBEF5IWvKriqkDLwgBFQAAAAAYASUAAMhCPQCAokN4AfABAfgB_gmAAtAFigIMCAAQARhWIE4oZTAP rs=AOn4CLDxj7JdxVRM1AirPYW7PfNremEz2Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/6Rhg9LTHfXk/hqdefault.jpg?sqp=-oaymwE9CNACELwBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYViBOKGUwDw== rs=AOn4CLBuibZLW6IAM-dgC57TaaxGslTWvQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"(Abstract Algebra 1) Definition of a Subgroup by learnifyable 152,074 views 11 years ago 10 minutes, 33 seconds"}},"simpleText":"(Abstract Algebra 1) Definition of a Subgroup"},"longBylineText":{"runs":[{"text":"learnifyable","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@learnifyable","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD3iLppPpQYyyDEcSlsNdOw","canonicalBaseUrl":"/@learnifyable"}}}]},"publishedTimeText":{"simpleText":"11 years ago"},"viewCountText":{"simpleText":"152,074 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"10 minutes, 33 seconds"}},"simpleText":"10:33"},"navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWRI-KvQg5Lak4mPAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=6Rhg9LTHfXk","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"6Rhg9LTHfXk","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=e91860f4b4c77d79 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1090000 mt=1741025593 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"learnifyable","navigationEndpoint":{"clickTrackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@learnifyable","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD3iLppPpQYyyDEcSlsNdOw","canonicalBaseUrl":"/@learnifyable"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_n4pSoUFHtU7k_K514FB54Fz4AVntHHAeozyeV0KuI=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBghA-fqdpsuemIzpAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"152K views"}},"simpleText":"152K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMYBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMYBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"6Rhg9LTHfXk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMYBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["6Rhg9LTHfXk"],"params":"CAQ%3D"}},"videoIds":["6Rhg9LTHfXk"]}},{"clickTrackingParams":"CMYBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMcBELlqIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},"popupType":"TOAST"}}]}},"trackingParams":"CMYBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBgg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgs2UmhnOUxUSGZYaw%3D%3D","commands":[{"clickTrackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBgg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMUBEI5iIhMItaK4tcPuiwMV4IP0Bx3kJwYI","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBgg=","hasSeparator":true}}],"trackingParams":"CMIBEKQwGAAiEwi1ori1w-6LAxXgg_QHHeQnBgg=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"10 minutes, 33 seconds"}},"simpleText":"10:33"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"6Rhg9LTHfXk","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMQBEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"6Rhg9LTHfXk"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMQBEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMMBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMMBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"6Rhg9LTHfXk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMMBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["6Rhg9LTHfXk"],"params":"CAQ%3D"}},"videoIds":["6Rhg9LTHfXk"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMMBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"(Abstract Algebra 1) Definition of a Subgroup - 10 minutes, 33 seconds - Go to channel - learnifyable - 152K views - 11 years ago - play video"}}}},{"compactVideoRenderer":{"videoId":"maACVONq5IU","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/maACVONq5IU/hqdefault.jpg?sqp=-oaymwE8CKgBEF5IWvKriqkDLwgBFQAAAAAYASUAAMhCPQCAokN4AfABAfgB_gmAAtAFigIMCAAQARhWIE4oZTAP rs=AOn4CLDVXhFyQ86Eyz_gp8mDn56zxB5WKw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/maACVONq5IU/hqdefault.jpg?sqp=-oaymwE9CNACELwBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYViBOKGUwDw== rs=AOn4CLCEfXGEMaTLvgFsNN8xKaLjJw0P3A","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"(Abstract Algebra 1) Definition of a Group by learnifyable 154,522 views 11 years ago 12 minutes, 25 seconds"}},"simpleText":"(Abstract Algebra 1) Definition of a Group"},"longBylineText":{"runs":[{"text":"learnifyable","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@learnifyable","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD3iLppPpQYyyDEcSlsNdOw","canonicalBaseUrl":"/@learnifyable"}}}]},"publishedTimeText":{"simpleText":"11 years ago"},"viewCountText":{"simpleText":"154,522 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"12 minutes, 25 seconds"}},"simpleText":"12:25"},"navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWRI-KvQg5Lak4mPAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=maACVONq5IU","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"maACVONq5IU","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=99a00254e36ae485 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=661250 mt=1741025593 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"learnifyable","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@learnifyable","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD3iLppPpQYyyDEcSlsNdOw","canonicalBaseUrl":"/@learnifyable"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_n4pSoUFHtU7k_K514FB54Fz4AVntHHAeozyeV0KuI=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBghAhcmrm87KgNCZAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"154K views"}},"simpleText":"154K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMABEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMABEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"maACVONq5IU","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMABEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["maACVONq5IU"],"params":"CAQ%3D"}},"videoIds":["maACVONq5IU"]}},{"clickTrackingParams":"CMABEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMEBELlqIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},"popupType":"TOAST"}}]}},"trackingParams":"CMABEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBgg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgttYUFDVk9OcTVJVQ%3D%3D","commands":[{"clickTrackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBgg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CL8BEI5iIhMItaK4tcPuiwMV4IP0Bx3kJwYI","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBgg=","hasSeparator":true}}],"trackingParams":"CLwBEKQwGAEiEwi1ori1w-6LAxXgg_QHHeQnBgg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"12 minutes, 25 seconds"}},"simpleText":"12:25"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"maACVONq5IU","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"maACVONq5IU"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL4BEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL0BEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CL0BEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"maACVONq5IU","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CL0BEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["maACVONq5IU"],"params":"CAQ%3D"}},"videoIds":["maACVONq5IU"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL0BEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"(Abstract Algebra 1) Definition of a Group - 12 minutes, 25 seconds - Go to channel - learnifyable - 154K views - 11 years ago - play video"}}}},{"compactVideoRenderer":{"videoId":"1jPaWx7jnIg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/1jPaWx7jnIg/hqdefault.jpg?sqp=-oaymwE8CKgBEF5IWvKriqkDLwgBFQAAAAAYASUAAMhCPQCAokN4AfABAfgB_gmAAtAFigIMCAAQARhYIE8oZTAP rs=AOn4CLA1Of09mEaqAo2dcBwRLEcpOJv5_g","width":168,"height":94},{"url":"https://i.ytimg.com/vi/1jPaWx7jnIg/hqdefault.jpg?sqp=-oaymwE9CNACELwBSFryq4qpAy8IARUAAAAAGAElAADIQj0AgKJDeAHwAQH4Af4JgALQBYoCDAgAEAEYWCBPKGUwDw== rs=AOn4CLDcpSO2jXsnytWppRuIvFS4TuPl5g","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"(Abstract Algebra 1) Groups of Permutations by learnifyable 129,070 views 8 years ago 17 minutes"}},"simpleText":"(Abstract Algebra 1) Groups of Permutations"},"longBylineText":{"runs":[{"text":"learnifyable","navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@learnifyable","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD3iLppPpQYyyDEcSlsNdOw","canonicalBaseUrl":"/@learnifyable"}}}]},"publishedTimeText":{"simpleText":"8 years ago"},"viewCountText":{"simpleText":"129,070 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"17 minutes, 32 seconds"}},"simpleText":"17:32"},"navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWRI-KvQg5Lak4mPAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=1jPaWx7jnIg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"1jPaWx7jnIg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=d633da5b1ee39c88 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=661250 mt=1741025593 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"learnifyable","navigationEndpoint":{"clickTrackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBggyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@learnifyable","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCD3iLppPpQYyyDEcSlsNdOw","canonicalBaseUrl":"/@learnifyable"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_n4pSoUFHtU7k_K514FB54Fz4AVntHHAeozyeV0KuI=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBghAiLmO97HL9pnWAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"129K views"}},"simpleText":"129K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLoBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLoBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"1jPaWx7jnIg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLoBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["1jPaWx7jnIg"],"params":"CAQ%3D"}},"videoIds":["1jPaWx7jnIg"]}},{"clickTrackingParams":"CLoBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLsBELlqIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},"popupType":"TOAST"}}]}},"trackingParams":"CLoBEP6YBBgFIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBgg=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgsxalBhV3g3am5JZw%3D%3D","commands":[{"clickTrackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBgg=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLkBEI5iIhMItaK4tcPuiwMV4IP0Bx3kJwYI","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBgg=","hasSeparator":true}}],"trackingParams":"CLYBEKQwGAIiEwi1ori1w-6LAxXgg_QHHeQnBgg=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"17 minutes, 32 seconds"}},"simpleText":"17:32"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLgBEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"1jPaWx7jnIg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLgBEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"1jPaWx7jnIg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLgBEPnnAxgBIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLcBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLcBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"1jPaWx7jnIg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLcBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["1jPaWx7jnIg"],"params":"CAQ%3D"}},"videoIds":["1jPaWx7jnIg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLcBEMfsBBgCIhMItaK4tcPuiwMV4IP0Bx3kJwYI"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"(Abstract Algebra 1) Groups of Permutations - 17 minutes - Go to channel - learnifyable - 129K views - 8 years ago - play video"}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/46SRJ_3bU_Y/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLBkeQOn4UwOPq9WikLMWA2MSMcsbg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/46SRJ_3bU_Y/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLC5c4TBq-okmMjwFDjKiPNnqrzI1g","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"46 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":2827827,"darkTheme":2827827}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":3551295,"darkTheme":3551295}}},"stackColor":{"lightTheme":8615065,"darkTheme":8550035}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Abstract Algebra 1"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"learnifyable

#############################