Infinite groups with many permutable subgroups

Adolfo Ballester-Bolinches; L. A. Kurdachenko; J. Otal; T. Pedraza

doi:10.4171/rmi/555

JournalsrmiVol. 24, No. 3pp. 745–764

Infinite groups with many permutable subgroups

Adolfo Ballester-Bolinches
Universitat de València, Burjassot (Valencia), Spain
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L. A. Kurdachenko
National Dnepropetrovsk University, Ukraine
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J. Otal
Universidad de Zaragoza, Spain
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T. Pedraza
Universidad Politécnica de Valencia, Spain
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- zbMATH Open

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Abstract

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 ( $A P$ -groups). We show that the structure of radical hyperfinite $A P$ -groups behave as that of finite soluble groups in which the relation to be a permutable subgroup is transitive ( $PT$ -groups).

Cite this article

Adolfo Ballester-Bolinches, L. A. Kurdachenko, J. Otal, T. Pedraza, Infinite groups with many permutable subgroups. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 745–764

DOI 10.4171/RMI/555