# Homework Help: Let G be a finite group. Under what circumstances

1. Oct 16, 2012

### Jamin2112

Let G be a finite group. Under what circumstances ....

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

... is that map δ:G→G defined by δ(x)=x2 an automorphism of F.

2. Relevant equations

And automorphism δ:G→G is a bijective homomorphism.

3. The attempt at a solution

The only circumstance I've so far found is that δ(x)≠x unless x=e. For

δ(x) = x -------> x2 = x -------> x = x2x-1 = xx-1 = e.

This seems to simple to be a sufficient condition, however.

Thoughts?

2. Oct 16, 2012

### micromass

Re: Let G be a finite group. Under what circumstances ....

What is the definition of an automorphism?? What properties must $\delta$ satisfy?

3. Oct 16, 2012

### Jamin2112

Re: Let G be a finite group. Under what circumstances ....

I stated the definition under relevant equations. And yes, I have a feeling where this is going ...

4. Oct 16, 2012

### I like Serena

Re: Let G be a finite group. Under what circumstances ....

So... first write down the conditions for homomorphism and bijective?
... and then write them down again, carefully substituting the symbols of your current problem?
And then... ;)