@inproceedings{Helleloid2006AlmostAP, title={Almost All p-Groups Have Automorphism Group a p-Group When p is Odd}, author={Geir T. Helleloid and Ursula Martin}, year={2006} }

- Published 2006

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups with automorphism group a p-group. Yet the goal of this paper is to prove that almost all finite p-groups do have automorphism group a p-group when p is odd. The asymptotic sense in which the theorem holds involves bounding the Frattini length of the p-groups and letting the number of generators go to infinity. The proof of the theorem draws on a detailed… CONTINUE READING