Divisibility results on the number of conjugacy classes in finite groups
type: Item
instance of: scholarly article
title: Divisibility results on the number of conjugacy classes in finite groups
zbMATH Open document ID: 0854.20033
DOI: 10.1007/BF01196162
author: Jason Fulman
published in: Archiv der Mathematik
publication date: 1997-01-20T00:00:00Z
review text: Let \(G\) be a finite group and let \(p_1,\dots,p_m\) be the primes dividing some integer \(n\). We show that the number of conjugacy classes of elements of order \(n\) is a multiple of \(\prod^m_{i=1}{p_i-1\over\text{gcd}(|G|,p_i-1)}\). We also relate the number of conjugacy classes \(k_G\) of \(G\) to \(k_N\), where \(N\) is a normal subgroup. These results yield corollaries related to the work of Mann and Vera Lopez.
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 938570
zbMATH Keywords: finite groups
zbMATH Keywords: number of conjugacy classes
zbMATH Keywords: elements of order \(n\)
zbMATH Keywords: normal subgroups
MaRDI profile type: Publication
cites work: Q5848209
cites work: Contemporary abstract algebra.
cites work: ON A THEOREM OF BURNSIDE
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
cites work: Conjugacy classes in finite solvable groups
full work available at URL: https://doi.org/10.1007/bf01196162
OpenAlex ID: W2067332608
description: scientific article; zbMATH DE number 938570