Revista Matemática Iberoamericana

Infinite groups with many permutable subgroups

Adolfo Ballester-Bolinches , Leonid A. Kurdachenko , Javier Otal , and Tatiana Pedraza

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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).

Article information

Rev. Mat. Iberoamericana, Volume 24, Number 3 (2008), 745-764.

First available in Project Euclid: 9 December 2008

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Primary: 20F99: None of the above, but in this section

radical groups hyper--$\mathfrak{X}$--groups $AP$--groups $PT$--groups


Ballester-Bolinches, Adolfo; Kurdachenko, Leonid A.; Otal, Javier; Pedraza, Tatiana. Infinite groups with many permutable subgroups. Rev. Mat. Iberoamericana 24 (2008), no. 3, 745--764.

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