Commutators of elements of coprime orders in finite groups

被引：13

作者：

Shumyatsky, Pavel ^{[1
]}

机构：

[1] Univ Brasilia, Dept Math, BR-70910900 Brasilia, DF, Brazil

来源：

FORUM MATHEMATICUM | 2015年 / 27卷 / 01期

关键词：

Finite groups; commutators; alternating groups;

D O I：

10.1515/forum-2012-0127

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is an attempt to find out which properties of a finite group G can be expressed in terms of commutators of elements of coprime orders. A criterion of solubility of G in terms of such commutators is obtained. We also conjecture that every element of a nonabelian simple group is a commutator of elements of coprime orders and we confirm this conjecture for the alternating groups.

引用

页码：575 / 583

页数：9

共 8 条

[1] A focal subgroup theorem for outer commutator words
Acciarri, Cristina
Fernandez-Alcober, Gustavo A.
Shumyatsky, Pavel
[J]. JOURNAL OF GROUP THEORY, 2012, 15 (03) : 397 - 405
[2] [Anonymous], 1967, Finite Groups
[3] The Ore conjecture
Liebeck, Martin W.
O'Brien, E. A.
Shalev, Aner
Tiep, Pham Huu
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2010, 12 (04) : 939 - 1008
[4] Robinson D.J.S., 1972, FINITENESS CONDITI 1
[5] Schmidt O.J., 1924, MAT SB, V31, P366
[6] Shumyatsky P., J AUST MATH IN PRESS
[7] NONSOLVABLE FINITE GROUPS ALL OF WHOSE LOCAL SUBGROUPS ARE SOLVABLE
THOMPSON, JG
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 74 (03) : 383 - &
[8] FITTING HEIGHT OF GROUPS AND OF FIXED-POINTS
TURULL, A
[J]. JOURNAL OF ALGEBRA, 1984, 86 (02) : 555 - 566

← 1 →