# Proving groups are isomorphic

1. Oct 25, 2009

### mariab89

1. The problem statement, all variables and given/known data

Recall that given a group G, we defined A(G) to be the set of all isomorphisms from G to itself; you proved that A(G) is a group under composition.
(a) Prove that A(Zn) is isomorphic to Zn/{0}
(b) Prove that A(Z) is isomorphic to Z2

2. Relevant equations

3. The attempt at a solution

2. Oct 25, 2009

### Dick

There aren't very many automorphisms of Z->Z. In fact, I think there is only two of them. For the other question, I'm not really sure what Z_n/{0} means. Can you explain?

3. Oct 25, 2009

### VeeEight

Can you figure out the sets A(Zn) and A(Z)?
The identity function is one that should come to mind.
Take a general function on Z by f(x)=bx for some b in Z. What values can b take on so that f(x) is a bijection?