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.
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页码：101 / 108
页数：8
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