Almost All p-Groups Have Automorphism Group a p-Group When p is Odd

@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}
}
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

1 Figure or Table

Topics