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Finite groups of even orders all of whose fourth maximal subgroups are weakly \(s_{2}\)-permutable

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Abstract

Let p be a prime number. A positive integer m is said to be a \(p'\)-number provided \(p\nmid m\). Let G be a finite group, and let H be a subgroup of G. We say that H is weakly \(s_{p}\)-permutable in G if G has a subnormal subgroup K such that G = HK, \(H_{sG}\leq K\) and \(|H\cap K:H_{sG}|\) is a \(p'\)-number, where \(H_{sG}\) is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We study the structure of a finite group G of even order all of whose fourth maximal subgroups are weakly \(s_{2}\)-permutable in G.

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  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    M. Asaad

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  1. M. Asaad
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Asaad, M. Finite groups of even orders all of whose fourth maximal subgroups are weakly \(s_{2}\)-permutable. Acta Math. Hungar. 167, 278–286 (2022). https://doi.org/10.1007/s10474-022-01228-z

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  • DOI: https://doi.org/10.1007/s10474-022-01228-z

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