On groups of odd order and p-rank \(\leq 2\)
type: Item
instance of: scholarly article
title: On groups of odd order and p-rank \(\leq 2\)
zbMATH Open document ID: 0666.20007
DOI: 10.1007/BF01197964
author: Yun Fan
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: Let \(R_ 2^{(p)}\) denote the set of groups of odd order and p-rank not exceeding 2. The purpose of this paper is to characterize minimal non- \(R_ 2^{(p)}\)-groups with trivial Frattini subgroup. Such groups are shown to be a semidirect product of an elementary abelian p-group, V, by a subgroup H of the general linear group on V, where there are nine possible types for H. The description of these types is too technical to give here.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 4089786
zbMATH Keywords: groups of odd order
zbMATH Keywords: p-rank
zbMATH Keywords: minimal non-\(R_ 2^{(p)}\)-groups
zbMATH Keywords: Frattini subgroup
zbMATH Keywords: semidirect product
reviewed by: Sheila Oates-Williams
MaRDI profile type: Publication
cites work: Q3789765
cites work: Q3955560
cites work: Endliche Gruppen I
cites work: Q3934684
cites work: Q4195124
cites work: Die Ordnungen, zu denen nur Gruppen mit gegebener Eigenschaft gehören
full work available at URL: https://doi.org/10.1007/bf01197964
OpenAlex ID: W2007031698
description: scientific article; zbMATH DE number 4089786