Small groups of automorphisms

Small groups of automorphisms Small groups of automorphisms

P. P. Pálfy and L. Pyber:

Small groups of automorphisms

We prove that any automorphism \alpha of a finite group G has order at most |G|-1 and if the order of \alpha is coprime to |G| then in fact \alpha has a regular orbit on G. We also show that if A is a group of automorphisms of G of coprime order then |A|<|G|^2.