Maximal subgroups and PST-groups

A subgroup H of a group G is said r 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 ar...

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Detalles Bibliográficos
Autores: Ballester-Bolinches, A., Beidleman, J.C., Esteban Romero, Ramón, Pérez-Calabuig, V.
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/43470
Acceso en línea:https://riunet.upv.es/handle/10251/43470
Access Level:acceso abierto
Palabra clave:Finite groups
Permutability
Sylow-permutability
Maximal subgroups
Supersolubility
MATEMATICA APLICADA
Descripción
Sumario:A subgroup H of a group G is said r 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 maxmial 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.