Paper 3, Section I, D

Groups | Part IA, 2013

Define what it means for a group to be cyclic, and for a group to be abelian. Show that every cyclic group is abelian, and give an example to show that the converse is false.

Show that a group homomorphism from the cyclic group CnC_{n} of order nn to a group GG determines, and is determined by, an element gg of GG such that gn=1g^{n}=1.

Hence list all group homomorphisms from C4C_{4} to the symmetric group S4S_{4}.

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