Odd order Hall subgroups of the classical linear groups
type: Item
instance of: scholarly article
title: Odd order Hall subgroups of the classical linear groups
zbMATH Open document ID: 0852.20014
DOI: 10.1007/BF02572618
author: Fletcher Gross
published in: Mathematische Zeitschrift
publication date: 1996-12-08T00:00:00Z
full work available at URL: https://eudml.org/doc/174813
review text: Let \(G\) be one of the finite classical linear groups, i.e., of the full linear groups, the symplectic groups, the orthogonal groups, and the unitary groups. It is proved that \(G\) has a Hall \(\pi\)-subgroup \((\pi\subseteq\pi(G)-\{2\})\) if, and only if, \(G\) has a Hall \(\{r,s\}\)-subgroup for each pair of distinct primes \(r\) and \(s\) in \(\pi\). A necessary and sufficient condition for a classical linear group to have a Hall \(\{r,s\}\)-subgroup, where \(r\) and \(s\) are distinct primes, dividing the order of \(G\), and \(2\notin\pi(G)\), is also obtained.
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 856568
zbMATH Keywords: finite classical linear groups
zbMATH Keywords: symplectic groups
zbMATH Keywords: orthogonal groups
zbMATH Keywords: unitary groups
zbMATH Keywords: Hall \(\pi\)-subgroups
reviewed by: N. M. Kurnosenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 856568