On the number of conjugacy classes of π-elements in finite groups

被引：6

作者：

Maroti, Attila ^{[1
,2
]}

Hung Ngoc Nguyen ^{[3
]}

机构：

[1] Alfred Renyi Inst Math, H-1053 Budapest, Hungary

[2] Tech Univ Kaiserslautern, Fachbereich Math, D-67653 Kaiserslautern, Germany

[3] Univ Akron, Dept Math, Akron, OH 44325 USA

来源：

ARCHIV DER MATHEMATIK | 2014年 / 102卷 / 02期

关键词：

Finite groups; Conjugacy classes; pi-elements; PROBABILITY;

D O I：

10.1007/s00013-014-0615-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group and pi be a set of primes. Put , where is the number of conjugacy classes of pi-elements in G and |G| (pi) is the pi-part of the order of G. In this paper we initiate the study of this invariant by showing that if then G possesses an abelian Hall pi-subgroup, all Hall pi-subgroups of G are conjugate, and every pi-subgroup of G lies in some Hall pi-subgroup of G. Furthermore, we have or . This extends and generalizes a result of W. H. Gustafson.

引用

页码：101 / 108

页数：8

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