Generalised mutually permutable products and saturated formations

[EN] We say that a group G = AB is the weakly mutually permutable product of the subgroups A and B, if A permutes with every subgroup of B containing A boolean AND B and B permutes with every subgroup of Acontaining A boolean AND B. We prove that some known results for mutually permutable products r...

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Detalles Bibliográficos
Autores: Ballester-Bolinches, A., Madanha, S. Y., Pedraza Aguilera, María Carmen|||0000-0003-0888-9310
Tipo de recurso: artículo
Fecha de publicación:2022
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:10251/194868
Acceso en línea:https://riunet.upv.es/handle/10251/194868
Access Level:acceso abierto
Palabra clave:Weakly mutually permutable products
Saturated formations
Residuals
MATEMATICA APLICADA
Descripción
Sumario:[EN] We say that a group G = AB is the weakly mutually permutable product of the subgroups A and B, if A permutes with every subgroup of B containing A boolean AND B and B permutes with every subgroup of Acontaining A boolean AND B. We prove that some known results for mutually permutable products remain true for weakly mutually permutable ones. Moreover, if G' is nilpotent, A permutes with every Sylow subgroup of Band B permutes with every Sylow subgroup of A, we show that G(F) = A(F) B-F, where F is a saturated formation containing U, the class of supersoluble groups. This generalises the corresponding result on mutually permutable products.