@article{a79acd0cfa014342a3a4f824a03044ff,
title = "The automorphism group of a finite p-group is almost always a p-group",
abstract = "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 whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism group of a finite p-group is almost always a p-group. The asymptotics in our theorem involve fixing any two of the following parameters and letting the third go to infinity: the lower p-length, the number of generators, and p. The proof of this theorem depends on a variety of topics: counting subgroups of a p-group; analyzing the lower p-series of a free group via its connection with the free Lie algebra; counting submodules of a module via Hall polynomials; and using numerical estimates on Gaussian coefficients.",
keywords = "p-Group, Automorphism group, Lower p-series, Frattini subgroup, Lower central p-series",
author = "Helleloid, {Geir T.} and Ursula Martin",
year = "2007",
doi = "10.1016/j.jalgebra.2007.01.008",
language = "English",
volume = "312",
pages = "294--329",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "1",
}