Abstract
According to Li and Zhao (Ukr Math J 64:102–109, 2012), a subgroup H of a finite group G is said to be \(S\Phi \)-supplemented in G if there exists a subnormal subgroup T of G such that \(G=HT\) and \(H\cap T\le \Phi (H)\), where \(\Phi (H)\) is the Frattini subgroup of H. In this paper, we extend the concept of \(S\Phi \)-supplemented subgroups, and give some criteria for (p-)hypercyclically embeddability of normal subgroups of finite groups by using fewer primary subgroups with given order. Our main results not only simplify, but also generalize some known theorems concerning \(S\Phi \)-supplemented subgroups.
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Acknowledgements
The authors are grateful to the referee who provided his/her valuable suggestions. Haoran Yu is supported by China Postdoctoral Science Foundation (Grant No. 2018M630317 and 2019T120231), National Natural Science Foundation of China (Grant No. 12001225 and 11871241), and The Education Department Project of Jilin Province (Grant No. JJKH20211033KJ). Xiaowei Xu is supported by National Natural Science Foundation of China (Grant No. 11971289).
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Yu, H., Xu, X. New criteria for hypercyclically embeddability of normal subgroups of finite groups. Ricerche mat 72, 153–158 (2023). https://doi.org/10.1007/s11587-021-00616-x
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DOI: https://doi.org/10.1007/s11587-021-00616-x