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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0222-z,
author = {Adolfo Ballester-Bolinches and James Beidleman and Ram\'on Esteban-Romero and Vicent P\'erez-Calabuig},
title = {Maximal subgroups and PST-groups},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1078-1082},
zbl = {1283.20016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0222-z}
}
Adolfo Ballester-Bolinches; James Beidleman; Ramón Esteban-Romero; Vicent Pérez-Calabuig. Maximal subgroups and PST-groups. Open Mathematics, Tome 11 (2013) pp. 1078-1082. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0222-z/
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