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?