Ejercicios resueltos de gruposTeoría de grupos 05

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ejercicios • 𝑃𝑟𝑢𝑒𝑏𝑒𝑠𝑒 𝑞𝑢𝑒 𝑠𝑖 𝐺 𝑒𝑠 𝑢𝑛 𝑔𝑟𝑢𝑝𝑜 𝑎𝑏𝑒𝑙𝑖𝑎𝑛𝑜, 𝑒𝑛𝑡𝑜𝑛𝑐𝑒𝑠, ∀𝑎,𝑏∈𝐺 𝑦 𝑡𝑜𝑑𝑜𝑠 𝑙𝑜𝑠 𝑒𝑛𝑡𝑒𝑟𝑜𝑠 𝑛, (𝑎𝑏)^𝑛=𝑎^𝑛 𝑏^𝑛. • 𝑆𝑖 𝐺 𝑒𝑠 𝑢𝑛 𝑔𝑟𝑢𝑝𝑜 𝑡𝑎𝑙 𝑞𝑢𝑒 ∀𝑎,𝑏∈𝐺 (𝑎𝑏)^2=𝑎^2 𝑏^2, 𝑑𝑒𝑚𝑢𝑒𝑠𝑡𝑟𝑒 𝑞𝑢𝑒 • 𝐺 𝑒𝑠 𝑎𝑏𝑒𝑙𝑖𝑎𝑛𝑜. • 𝑆𝑖 𝐺 𝑒𝑠 𝑢𝑛 𝑔𝑟𝑢𝑝𝑜 𝑒𝑛 𝑒𝑙 𝑞𝑢𝑒 〖(𝑎𝑏)〗^𝑛=𝑎^𝑛 𝑏^𝑛 𝑝𝑎𝑟𝑎 𝑡𝑟𝑒𝑠 𝑒𝑛𝑡𝑒𝑟𝑜𝑠 • 𝑐𝑜𝑛𝑠𝑒𝑐𝑢𝑡𝑖𝑣𝑜𝑠 𝑛 𝑦 𝑝𝑎𝑟𝑎 𝑡𝑜𝑑𝑜𝑠 𝑙𝑜𝑠 𝑎,𝑏∈𝐺, 𝑑𝑒𝑚𝑢𝑒𝑠𝑡𝑟𝑒 𝑞𝑢𝑒 𝐺 𝑒𝑠 𝑎𝑏𝑒𝑙𝑖𝑎𝑛𝑜 • Bibliografía • Herstein, I.N., Álgebra Moderna, México : Editorial Trillas, 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