Infinite groups with many permutable subgroups
Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, p. 745-764 / Harvested from Project Euclid
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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).
Publié le : 2008-04-15
Classification:  radical groups,  hyper--$\mathfrak{X}$--groups,  $AP$--groups,  $PT$--groups,  20F99 
@article{1228834293,
     author = {Ballester-Bolinches
,  
Adolfo and Kurdachenko
,  
Leonid A. and Otal
,  
Javier and Pedraza
,  
Tatiana},
     title = {Infinite groups with many permutable subgroups},
     journal = {Rev. Mat. Iberoamericana},
     volume = {24},
     number = {2},
     year = {2008},
     pages = { 745-764},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1228834293}
}

Ballester-Bolinches
,  
Adolfo; Kurdachenko
,  
Leonid A.; Otal
,  
Javier; Pedraza
,  
Tatiana. Infinite groups with many permutable subgroups. Rev. Mat. Iberoamericana, Tome 24 (2008) no. 2, pp.  745-764. http://gdmltest.u-ga.fr/item/1228834293/