The radical subgroups of the Fischer simple groups
type: Item
instance of: scholarly article
title: The radical subgroups of the Fischer simple groups
zbMATH Open document ID: 1014.20007
DOI: 10.1016/S0021-8693(02)00119-9
author: Masaaki Kitazume
author: Satoshi Yoshiara
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: A \(p\)-subgroup of a group \(G\) is called radical if it is the largest normal \(p\)-subgroup of its normalizer. The present paper classifies the conjugacy classes of \(p\)-radical subgroups in the sporadic Fischer groups \(Fi_{22}\) and \(Fi_{24}'\) for \(p=2\) and \(3\). The other Fischer group has been dealt with by \textit{J. An} and \textit{E. A. O'Brien} [Int. J. Algebra Comput. 9, No. 6, 621-670 (1999; Zbl 0949.20010)]. Primes greater than \(3\) are easy, and the remaining sporadic groups (except the Monster and Baby Monster) are dealt with in other papers by the second author [see J. Algebra 233, No. 1, 309-341 (2000; Zbl 0966.20008)].
Mathematics Subject Classification ID: 20D08
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 1867991
zbMATH Keywords: normal \(p\)-subgroups
zbMATH Keywords: conjugacy classes
zbMATH Keywords: \(p\)-radical subgroups
zbMATH Keywords: sporadic Fischer groups
zbMATH Keywords: sporadic groups
reviewed by: Robert A. Wilson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1867991