ON THE PRODUCT OF TWO π-DECOMPOSABLE SOLUBLE GROUPS

被引：6

作者：

Kazarin, L. S. ^{[1
]}

Martinez-Pastor, A. ^{[2
,3
]}

Perez-Ramos, M. D. ^{[4
]}

机构：

[1] Yaroslavl P Demidov State Univ, Dept Math, Yaroslavl 150000, Russia

[2] Univ Politecn Valencia, Dept Matemat Aplicada, Escuela Tecn Super Informat Aplicada, Valencia 46022, Spain

[3] Univ Politecn Valencia, IMPA UPV, Valencia 46022, Spain

[4] Univ Valencia, Dept Algebra, E-46100 Valencia, Spain

来源：

PUBLICACIONS MATEMATIQUES | 2009年 / 53卷 / 02期

关键词：

Products of groups; pi-decomposable groups; Hall subgroups; SUBGROUPS;

D O I：

10.5565/PUBLMAT_53209_07

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let the group G = AB be a product of two pi-decomposable subgroups A = O-pi(A) x O-pi'(A) and B = O-pi(B) x O-pi'(B) where pi is a set of primes. The authors conjecture that O-pi(A)O-pi(B) = O-pi(B)O-pi(A) if pi is a set of odd primes. In this paper it is proved that the conjecture is true if A and B are soluble. A similar result with certain additional restrictions holds in the case 2 is an element of pi. Moreover, it is shown that the conjecture holds if O-pi'(A) and O-pi'(B) have coprime orders.

引用

页码：439 / 456

页数：18