Infinite groups with many permutable subgroups

被引：22

作者：

Ballester-Bolinches, A. ^{[1
]}

Kurdachenko, L. A. ^{[2
]}

Otal, J. ^{[3
]}

Pedraza, T. ^{[4
]}

机构：

[1] Univ Valencia, Dept Algebra, E-46100 Burjassot, Valencia, Spain

[2] Natl Dnepropetrovsk Univ, Dept Algebra, UA-49050 Dnepropetrovsk, Ukraine

[3] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

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

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2008年 / 24卷 / 03期

关键词：

Radical groups; hyper-chi-groups; AP-groups; PT-groups;

D O I：

10.4171/RMI/555

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subgroup H of a group G is said to be permutable in G, if HK = KH for every subgroup K of G. A result due to Stonehewer asserts that every permutable subgroup is ascendant although the converse is false. In this paper we study some infinite groups whose ascendant subgroups are permutable (AP-groups). We show that the structure of radical hyperfinite AP-groups behave as that of finite soluble groups in which the relation to be a permutable subgroup is transitive (PT-groups).

引用

页码：745 / 764

页数：20

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