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

共 50 条

[31] A note on conjugacy classes of finite groups
Kalra, Hemant
Gumber, Deepak
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2014, 124 (01): : 31 - 36
[32] CONJUGACY CLASSES IN FINITE-GROUPS
MANN, A
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1978, 31 (01) : 78 - 84
[33] Notes on conjugacy classes of finite groups
Chen, Xiaoyou
Wang, Huiqun
[J]. JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2018, 21 (7-8): : 1519 - 1522
[34] A NOTE ON CONJUGACY CLASSES OF FINITE GROUPS
You, Xingzhong
[J]. GEORGIAN MATHEMATICAL JOURNAL, 2008, 15 (04) : 799 - 803
[35] CONJUGACY CLASSES IN FINITE-GROUPS
LOPEZ, AV
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1987, 105 : 259 - 264
[36] On Finite Groups with Special Conjugacy Classes
杜祥林
[J]. Railway Engineering Science, 2007, (02) : 172 - 174
[37] On groups with finite verbal conjugacy classes
Franciosi, S
de Giovanni, F
Shumyatsky, P
[J]. HOUSTON JOURNAL OF MATHEMATICS, 2002, 28 (04): : 683 - 689
[38] On powers of conjugacy classes in finite groups
Beltran, Antonio
[J]. JOURNAL OF GROUP THEORY, 2022, 25 (05) : 965 - 971
[39] A note on conjugacy classes of finite groups
HEMANT KALRA
DEEPAK GUMBER
[J]. Proceedings - Mathematical Sciences, 2014, 124 : 31 - 36
[40] THE NUMBER OF CONJUGACY CLASSES OF ELEMENTS OF THE CREMONA GROUP OF SOME GIVEN FINITE ORDER
Blanc, Jeremy
[J]. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2007, 135 (03): : 419 - 434

← 1 2 3 4 5 →