Conjugacy classes in finite solvable groups
type: Item
instance of: scholarly article
title: Conjugacy classes in finite solvable groups
zbMATH Open document ID: 0533.20007
DOI: 10.1007/BF02760519
published in: Israel Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In this note the number of conjugacy classes in a finite solvable group is obtained as a function of any type of the composition factors of G. It results in a new elementary proof of one of Mann's results for solvable groups and that result is improved here for some classes of groups. \textit{A. Mann}'s result [Isr. J. Math. 31, 78-84 (1978)] is: \(| G| \equiv r(G)(mod ab),\) where \(| G| =p_ 1\!^{e_ 1}...p_ t\!^{e_ t}\), \(p_ i\) prime and \(p_ i\neq p_ j\) for every \(i\neq j\), \(r(G)=number\) of conjugacy classes of G, \(a=g.c.d.(p_ 1-1,...,p_ t-1), b=g.c.d.(p_ 1\!^ 2-1,...,p_ t\!^ 2-1).\)
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 3845822
zbMATH Keywords: number of conjugacy classes
zbMATH Keywords: finite solvable group
zbMATH Keywords: composition factors
author: A. Vera-López
reviewed by: Robert W. van der Waall
MaRDI profile type: Publication
cites work: Q5848209
cites work: Q5551256
cites work: ON A THEOREM OF BURNSIDE
cites work: Endliche Gruppen I
cites work: Conjugacy classes in finite groups
cites work: Two problems on finite groups with k conjugate classes
cites work: On a theorem of Burnside
full work available at URL: https://doi.org/10.1007/bf02760519
OpenAlex ID: W2017638245
Recommended article: Conjugacy classes of finite solvable subgroups in Lie groups
Recommended article: On The Number of Conjugacy Classes of a Finite Solvable Group
Recommended article: Conjugacy classes in finite groups
Recommended article: Conjugacy class sizes and solvability of finite groups.
Recommended article: Lengths of conjugacy classes of finite solvable groups
Recommended article: Conjugacy class sizes of some elements and solvability of finite groups.
Recommended article: The conjugacy classes in a finite simple group.
description: scientific article; zbMATH DE number 3845822