ON THE ORDER OF THE AUTOMORPHISM GROUP OF A FINITE GROUP

We show that if vertical bar Aut(G)vertical bar is odd, then without loss of generality we may assume the only primes dividing vertical bar G vertical bar are those dividing vertical bar Aut(G)vertical bar. We also classify finite abelian groups A such that vertical bar Aut(A)vertical bar = vertical bar A vertical bar and finite abelian groups A such that vertical bar Aut(A)vertical bar(p) = vertical bar A vertical bar(p), where p is a prime dividing vertical bar A vertical bar.