Let G be a finite group. Under what circumstances

[Jamin2112]

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

Homework Statement

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

Homework Equations

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

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?

 

[micromass]

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

 

[Jamin2112]

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

 

[I like Serena]

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... ;)