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Unformatted text preview: f ( n ) = a n . If a has nite order prove that ker f = h a i . Exercise 7. Let G be an abelian group and let n Z . Dene f : G G by f ( x ) = x n . a. Prove that f is a homomorphism. b. Compute ker f . c. Use f to show that { y G  y = x n for some x G } is a subgroup of G...
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This note was uploaded on 02/29/2012 for the course MATH 3362 taught by Professor Ryandaileda during the Spring '10 term at Trinity University.
 Spring '10
 RyanDaileda
 Algebra

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