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The influence of weakly pronormal subgroups on the supersolvability of finite groups

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Abstract

Let G be a finite group and H a subgroup of G. We say that H is pronormal in G if for every \(g\in G\), the subgroups H and \(H^g\) are conjugate in \(\langle H,H^{g} \rangle\); H is called weakly pronormal in G if there exists a subgroup K of G such that G = HK and \(H\cap K\) is pronormal in G. In this paper, we investigate the structure of G under the assumption that certain subgroups of G are weakly pronormal in G. Our results improve and generalize new recent results in the literature.

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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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Correspondence to M. Asaad.

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Asaad, M. The influence of weakly pronormal subgroups on the supersolvability of finite groups. Acta Math. Hungar. 170, 655–660 (2023). https://doi.org/10.1007/s10474-023-01352-4

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  • DOI: https://doi.org/10.1007/s10474-023-01352-4

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