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 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 \textit{to be a permutable subgroup} is transitive ($PT$--groups).
Citation
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.
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