On finite groups with restrictions on centralizers
type: Item
instance of: scholarly article
title: On finite groups with restrictions on centralizers
zbMATH Open document ID: 1027.20010
DOI: 10.1023/A:1014867428484
author: Yanyan Li
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Let \(G\) be a finite group and \(H\) a subgroup of \(G\). Denote by \(w(n)\) the number of factors in a representation of a positive integer \(n\) as a product of primes, \(w(H)=w(|H|)\) and \(v(G)=\max\{w(C(g))\mid g\in G\setminus Z(G)\}\), where \(C(g)\) is the centralizer of \(g\) in \(G\). The finite groups satisfying the condition \(v(G)=2\) and \(v(G)=3\) were described by \textit{M. Bianchi} and \textit{O. Manz} [Boll. Unione. Mat. Ital., VII. Ser., A 4, No. 7, 365-370 (1990; Zbl 0717.20019)] and \textit{A. Scarselli} [Boll. Unione Mat. Ital., VII. Ser., B 6, No. 3, 649-663 (1992; Zbl 0793.20016)]. In this paper, the authors present a complete description of finite groups such that \(v(G)=4\) (For the case of center-free finite groups, see the authors [Mat. Zametki 69, No. 5, 643-655 (2001; Zbl 0997.20030)]).
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D10
zbMATH DE Number: 1928188
zbMATH Keywords: centralizers
zbMATH Keywords: Schur multipliers
zbMATH Keywords: Frobenius groups
zbMATH Keywords: nilpotent groups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: finite groups
reviewed by: Shi Wujie
MaRDI profile type: Publication
full work available at URL: a:1014867428484
OpenAlex ID: W87362274
description: scientific article; zbMATH DE number 1928188