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Groups with all subgroups permutable or of finite rank

100%
Dixon M., Karatas Y.
Open Mathematics
|
2012
|
tom 10
|
nr 3
950-957
EN
In this paper we investigate the structure of X-groups in which every subgroup is permutable or of finite rank. We show that every subgroup of such a group is permutable.
2
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Algorithms for permutability in finite groups

63%
Ballester-Bolinches A., Cosme-Llópez E., Esteban-Romero R.
Open Mathematics
|
2013
|
tom 11
|
nr 11
1914-1922
EN
In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.
3
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Groups whose all subgroups are ascendant or self-normalizing

63%
Kurdachenko L., Otal J., Russo A., Vincenzi G.
Open Mathematics
|
2011
|
tom 9
|
nr 2
420-432
EN
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16].
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