Most small \(p\)-groups have an automorphism of order 2
type: Item
instance of: scholarly article
title: Most small \(p\)-groups have an automorphism of order 2
zbMATH Open document ID: 1366.20011
author: Joshua Maglione
published in: Archiv der Mathematik
publication date: 2017-03-23T00:00:00Z
review text: 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.
reviewed by: Gernot Stroth
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D45
zbMATH DE Number: 6696923
zbMATH Keywords: \(p\)-groups
describes a project that uses: LiePRing
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: s00013-016-1005-0
OpenAlex ID: W2562957045
cites work: The Magma algebra system. I: The user language
cites work: A fast isomorphism test for groups whose Lie algebra has genus 2
cites work: Groups acting on tensor products.
cites work: The automorphism group of a finite \(p\)-group is almost always a \(p\)-group.
cites work: Efficient characteristic refinements for finite groups
cites work: Q4946828
cites work: Almost all 𝑝-groups have automorphism group a 𝑝-group
cites work: Groups and nilpotent Lie rings whose order is the sixth power of a prime.
cites work: The groups with order \(p^7\) for odd prime \(p\).
cites work: More characteristic subgroups, Lie rings, and isomorphism tests for p-groups
DOI: 10.1007/S00013-016-1005-0
description: scientific article; zbMATH DE number 6696923