Generalised mutually permutable products and saturated formations, II
[EN] 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 $A \cap B$ and B permutes with every subgroup of A containing $A \cap B$ . Weakly mutually permutable products were introduced by the first, second and fourth aut...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2024 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/203725 |
| Online Access: | https://riunet.upv.es/handle/10251/203725 |
| Access Level: | Open access |
| Keyword: | Weakly mutually permutable products Supersoluble groups Saturated formations Projectors Normalisers MATEMATICA APLICADA |
| Summary: | [EN] 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 $A \cap B$ and B permutes with every subgroup of A containing $A \cap B$ . Weakly mutually permutable products were introduced by the first, second and fourth authors ['Generalised mutually permutable products and saturated formations', J. Algebra 595 (2022), 434-443] who showed that if $G'$ is nilpotent, A permutes with every Sylow subgroup of B and B permutes with every Sylow subgroup of A, then $G<^>{\mathfrak {F}}=A<^>{\mathfrak {F}}B<^>{\mathfrak {F}} $ , where $ \mathfrak {F} $ is a saturated formation containing $ \mathfrak {U} $ , the class of supersoluble groups. In this article we prove results on weakly mutually permutable products concerning $ \mathfrak {F} $ -residuals, $ \mathfrak {F} $ -projectors and $\mathfrak {F}$ -normalisers. As an application of some of our arguments, we unify some results on weakly mutually $sn$ -products. |
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