# hw26 - f p of the preceding exercise is not onto Conclude...

This preview shows page 1. Sign up to view the full content.

Modern Algebra 1 Homework 12.3 Spring 2010 Due April 21 Exercise 5. Let G be an (additive) abelian group and let m Z . a. Prove that the function f m : G G given by f m ( x ) = mx is a homomorphism. b. Use part a to show that G m and mG = { mx | x G } are both subgroups of G . c. If G is ﬁnite, under what conditions on m and | G | is f m injective? Exercise 6. If p is a prime and G is an abelian p -group, show that the homomorphism
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: f p of the preceding exercise is not onto. Conclude that | pG | < | G | . Exercise 7. If p is a prime and n ∈ N prove that p Z p n ∼ = Z p n-1 . [ Suggestion: Use the homomorphism f p of exercise 5 and the fact that subgroups of cyclic groups are cyclic.]...
View Full Document

## 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.

Ask a homework question - tutors are online