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November, 2008 Infinite groups with many permutable subgroups
Adolfo Ballester-Bolinches , Leonid A. Kurdachenko , Javier Otal , Tatiana Pedraza
Rev. Mat. Iberoamericana 24(3): 745-764 (November, 2008).

Abstract

A subgroup $H$ of a group $G$ is said to be \textit{permutable in$G$}, if $HK = KH$ for every subgroup $K$ of $G$. A result due toStonehewer asserts that every permutable subgroup is ascendantalthough the converse is false. In this paper we study someinfinite 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 therelation \textit{to be a permutable subgroup} is transitive($PT$--groups).

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Adolfo Ballester-Bolinches . Leonid A. Kurdachenko . Javier Otal . Tatiana Pedraza . "Infinite groups with many permutable subgroups." Rev. Mat. Iberoamericana 24 (3) 745 - 764, November, 2008.

Information

Published: November, 2008
First available in Project Euclid: 9 December 2008

zbMATH: 1175.20036
MathSciNet: MR2490161

Subjects:
Primary: 20F99

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.24 • No. 3 • November, 2008
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