The overgroups of the solvable subgroup of maximal order in \(S_ n\)
type: Item
instance of: scholarly article
title: The overgroups of the solvable subgroup of maximal order in \(S_ n\)
zbMATH Open document ID: 0676.20002
DOI: 10.1007/BF01237564
author: Yoav Segev
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: \textit{A. Mann} [Isr. J. Math. 55, 162-172 (1986; Zbl 0609.20015)] determined the solvable subgroups of maximal order in the symmetric group \(S_ n\). In this note the structure of the overgroups of such subgroups is given. In his Ph. D. Thesis the author stated that the Borel subgroup of a finite simple group of Lie type can be characterized as the solvable subgroup of maximal order (excluded the groups defined over the fields of order 2, 3, 5 and 7), therefore the appropriate overgroups in the finite simple groups of Lie type over the fields of sufficiently large orders are the parabolic subgroups.
Mathematics Subject Classification ID: 20B35
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 4107070
zbMATH Keywords: solvable subgroups of maximal order
zbMATH Keywords: symmetric group
zbMATH Keywords: overgroups
zbMATH Keywords: Borel subgroup
zbMATH Keywords: finite simple groups of Lie type
zbMATH Keywords: parabolic subgroups
reviewed by: Andreiy Kondrat'yev
MaRDI profile type: Publication
cites work: Soluble subgroups of symmetric and linear groups
full work available at URL: https://doi.org/10.1007/bf01237564
OpenAlex ID: W2063601815
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description: scientific article; zbMATH DE number 4107070