Most small \(p\)-groups have an automorphism of order 2. (English) Zbl 1366.20011

Maglione, Joshua

Arch. Math. 108, No. 3, 225-232 (2017).

Let \(f(p,n)\) be the number of isomorphism types of \(p\)-groups of order \(p^n\) and \(g(p,n)\) the number of those, whose automorphism group is a \(p\)-group. There is a conjecture that \(g(p,n)/f(p,n)\) goes to \(1\) with \(n\) to \(\infty\). In this paper, the author considers the question that \(p\) goes to \(\infty\) and \(n =6\) or \(7\). The result of the paper is that the limit will be \(1/3\). For the proof, the author uses Lie-ring methods. The reviewer could not see the relation between the title and the contents of the paper.

Reviewer: Gernot Stroth (Halle)

MSC:

20D15	Finite nilpotent groups, \(p\)-groups
20D45	Automorphisms of abstract finite groups

Keywords:

\(p\)-groups

Software:

Magma; LiePRing

References:

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