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Maximal subgroups and PST-groups

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Ballester-Bolinches A., Beidleman J., Esteban-Romero R., Pérez-Calabuig V.

Open Mathematics

2013

tom 11

nr 6

1078-1082

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19–25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions of Kaplan’s results, which enables a better understanding of the relationships between these classes.

Ograniczanie wyników

1 Open Mathematics

1 Ballester-Bolinches A.

1 Beidleman J.

1 Esteban-Romero R.

1 Pérez-Calabuig V.

1 2013

Wyniki wyszukiwania

Maximal subgroups and PST-groups