Abstract Algebra Homomorphisms and Quotient Groups

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>> YOUR LINK HERE: ___ http://youtube.com/watch?v=2LGGSsXmXJY

This video uses the Rubiks Cube to illustrate the notion of a homomorphism -- the type of function in group theory that preserves the operation on a group. It is noted that every homomorphism sends some of the elements of the domain group to the identity element of the codomain group. This collection of elements always forms a NORMAL subgroup of the domain group. Furthermore, the collection of COSETS of this normal subgroup form a group that is isomorphic to a subgroup of the codomain group. Berry College professor emeritus Dr. Eric McDowell (a.k.a. ‪@theMathSinger‬) provides examples of homomorphisms, and explains the connection between quotient groups and homomorphic images.

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