Some classes of finite groups and mutually permutable products

[EN] This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G=AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every subgroup of the other factor. We prove that mutually permutable products of Y-grou...

Descripción completa

Detalles Bibliográficos
Autores: Asaad, Mohamed, Ballester Bolinches, Adolfo, Beidleman, James C., Esteban Romero, Ramón
Tipo de recurso: artículo
Fecha de publicación:2008
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:10251/19092
Acceso en línea:https://riunet.upv.es/handle/10251/19092
Access Level:acceso abierto
Palabra clave:Mutually permutable product
Permutability
Y-group
Pst-group
Sc-group
Finite group
MATEMATICA APLICADA
Descripción
Sumario:[EN] This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G=AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every subgroup of the other factor. We prove that mutually permutable products of Y-groups (groups satisfying a converse of Lagrange's theorem) and SC-groups (groups whose chief factors are simple) are SC-groups, by means of a local version. Next we show that the product of pairwise mutually permutable Y-groups is supersoluble. Finally, we give a local version of the result stating that when a mutually permutable product of two groups is a PST-group (that is, a group in which every subnormal subgroup permutes with all Sylow subgroups), then both factors are PST-groups.