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...
| Autores: | , , |
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| 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 |
| 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. |
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