Archiv der Mathematik

, Volume 108, Issue 3, pp 225–232 | Cite as

Most small \({\varvec{p}}\)-groups have an automorphism of order 2

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Abstract

Let f(pn) be the number of pairwise nonisomorphic p-groups of order \(p^n\), and let g(pn) be the number of groups of order \(p^n\) whose automorphism group is a p-group. We prove that the limit, as p grows to infinity, of the ratio g(pn) / f(pn) equals 1/3 for \(n=6,7\).

Keywords

Lie rings Isoclinism 

Mathematics Subject Classification

20D15 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of MathematicsColorado State UniversityFort CollinsUSA

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