Abstract
Let G be a finite group and H a subgroup of G. H is said to be NH-embedded in G if there exists a normal subgroup T of G such that HT is a Hall subgroup of G and \(H \cap T \le H_{{\overline{s}}G}\), where \(H_{{\overline{s}}G}\) is the largest s-semipermutable subgroup of G contained in H, and H is said to be S-quasinormally embedded in G provided every Sylow subgroup of H is a Sylow subgroup of some S-quasinormal subgroup of G. In this paper, we obtain some criteria for p-nilpotency and Supersolvability of a finite group and extend some known results concerning NH-embedded and S-quasinormally embedded subgroups.
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Acknowledgements
W. Zheng is supported by Innovation Project of GUET Graduate Education (2023YCXS112). W. Meng is supported by National Natural Science Foundation of China (12161021), Guangxi Natural Science Foundation Program (2021JJA10003), Center for Applied Mathematics of Guangxi (GUET) and Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation. J.K. Lu is supported by National Natural Science Foundation of China (11861015) and Guangxi Natural Science Foundation Program (2020GXNSFAA238045).
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Zheng, W., Cui, L., Meng, W. et al. On NH-embedded and S-quasinormally embedded subgroups of finite groups. Boll Unione Mat Ital 17, 67–73 (2024). https://doi.org/10.1007/s40574-023-00379-3
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DOI: https://doi.org/10.1007/s40574-023-00379-3