On finite groups with nilpotent Sylow-normalizers
type: Item
instance of: scholarly article
title: On finite groups with nilpotent Sylow-normalizers
zbMATH Open document ID: 0605.20017
DOI: 10.1007/BF01191993
author: Mariagrazia Bianchi
author: Anna Gillio Berta Mauri
author: Peter Hauck
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: It is well known that every finite solvable group possesses a unique conjugacy class of nilpotent self-normalizing subgroups, the so-called Carter subgroups, but it is an open question whether every finite group possesses at most one conjugacy class of Carter subgroups. In this paper, the authors consider the following problem, as a special case of the question above: Is it true that in every finite group G the set \(n(G)=\{N_ G(P)|\) P a Sylow p-subgroup of G for some prime p such that \(N_ G(P)\) is nilpotent\(\}\) is a (possibly empty) set of conjugate subgroups of G? They prove that the answer to this problem is ''yes'' provided the statement is true for all groups G of the form Inn(E)\(\leq G\leq Aut(E)\) where E is a non-abelian finite simple group.
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 3977241
zbMATH Keywords: finite solvable group
zbMATH Keywords: nilpotent self-normalizing subgroups
zbMATH Keywords: conjugacy class of Carter subgroups
reviewed by: Rodica Covaci
MaRDI profile type: Publication
cites work: Q4100285
cites work: Projektive Klassen endlicher Gruppen. I: Schunck- und Gaschützklassen
cites work: Q5639863
cites work: Endliche Gruppen I
cites work: Q3934684
cites work: On finite insoluble groups with nilpotent maximal subgroups
cites work: Q5549108
cites work: FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER
cites work: A special class of non-solvable groups
description: scientific article; zbMATH DE number 3977241