Most small p -groups have an automorphism of order 2

Joshua Maglione

doi:10.1007/s00013-016-1005-0

Most small p -groups have an automorphism of order 2

Joshua Maglione

Colorado State University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

Abstract

Let f(p, n) be the number of pairwise nonisomorphic p-groups of order pⁿ, and let g(p, n) be the number of groups of order pⁿ 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.

Original language	English
Pages (from-to)	225-232
Number of pages	8
Journal	Archiv der Mathematik
Volume	108
Issue number	3
DOIs	https://doi.org/10.1007/s00013-016-1005-0
Publication status	Published - 1 Mar 2017
Externally published	Yes

Keywords

Isoclinism
Lie rings

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10.1007/s00013-016-1005-0

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title = "Most small p -groups have an automorphism of order 2",

abstract = "Let f(p, n) be the number of pairwise nonisomorphic p-groups of order pn, and let g(p, n) be the number of groups of order pn 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.",

keywords = "Isoclinism, Lie rings",

author = "Joshua Maglione",

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AU - Maglione, Joshua

PY - 2017/3/1

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N2 - Let f(p, n) be the number of pairwise nonisomorphic p-groups of order pn, and let g(p, n) be the number of groups of order pn 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.

AB - Let f(p, n) be the number of pairwise nonisomorphic p-groups of order pn, and let g(p, n) be the number of groups of order pn 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.

KW - Isoclinism

KW - Lie rings

UR - https://www.scopus.com/pages/publications/85006470361

U2 - 10.1007/s00013-016-1005-0

DO - 10.1007/s00013-016-1005-0

M3 - Article

SN - 0003-889X

VL - 108

SP - 225

EP - 232

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 3

ER -

Most small p -groups have an automorphism of order 2

Abstract

Keywords

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