Sylow intersections in finite groups
type: Item
instance of: scholarly article
title: Sylow intersections in finite groups
zbMATH Open document ID: 0932.20018
author: Ben Brewster
author: Peter Hauck
published in: Journal of Algebra
publication date: 1998-11-29T00:00:00Z
review text: The meet semilattice generated by \(\text{Syl}_p(G)\) within the subgroup lattice of a finite group \(G\) is studied, where \(p\) is a fixed prime. The main result implies that if \(p\) is an odd non-Mersenne prime, \(G\) is a finite \(p\)-solvable group, and \(P_1\), \(P_2\), \(P_3\) are Sylow \(p\)-subgroups of \(G\), then \(G\) possesses a Sylow \(p\)-subgroup \(P_4\) such that \(P_1\cap P_4=P_1\cap P_2\cap P_3\). It is shown that if \(p=2\) or \(p\) is Mersenne, \(G\) is a finite \(p\)-solvable group, then the intersection of any four Sylow \(p\)-subgroups can be obtained as the intersection of three Sylow \(p\)-subgroups with one Sylow \(p\)-subgroup in common.
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 1214152
zbMATH Keywords: meet semilattices
zbMATH Keywords: subgroup lattices
zbMATH Keywords: finite groups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: finite \(p\)-solvable groups
reviewed by: N. M. Kurnosenko
MaRDI profile type: Publication
full work available at URL: jabr.1998.7426
OpenAlex ID: W2041968480
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DOI: 10.1006/JABR.1998.7426
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description: scientific article; zbMATH DE number 1214152