The centre of a finite group
type: Item
instance of: scholarly article
title: The centre of a finite group
zbMATH Open document ID: 0597.20010
DOI: 10.1007/BF01189277
author: T. A. Peng
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: Let G be a finite group. Let p be a prime and let \(C_ p\) be the set of all proper subgroups of G whose order is divisible by at most two distinct primes, one of which is p. Let \(Z(X)_ p\) be the Sylow p- subgroup of the centre of the group X. If \(Z(H)_ p\neq 1\) for all subgroups H in \(C_ p\), then either \(Z(G)_ p\neq 1\) or G is a \(\{\) p,q\(\}\)-group with q a prime distinct from p.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D20
zbMATH DE Number: 3961935
zbMATH Keywords: Sylow p-subgroup
zbMATH Keywords: centre
zbMATH Keywords: \(\{\) p,q\(\}\)-group
MaRDI profile type: Publication
cites work: Endliche Gruppen I
cites work: Some Analogues of Glauberman's Z ∗ -Theorem
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description: scientific article; zbMATH DE number 3961935