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

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Abstract

Let f(p, n) be the number of pairwise nonisomorphic p-groups of order \(p^n\), and let g(p, n) 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(p, n) / f(p, n) equals 1/3 for \(n=6,7\).

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  1. Department of Mathematics, Colorado State University, Fort Collins, CO, 80523, USA

    Joshua Maglione

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  1. Joshua Maglione
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Correspondence to Joshua Maglione.

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Maglione, J. Most small \({\varvec{p}}\)-groups have an automorphism of order 2. Arch. Math. 108, 225–232 (2017). https://doi.org/10.1007/s00013-016-1005-0

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  • DOI: https://doi.org/10.1007/s00013-016-1005-0

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