New criteria for hypercyclically embeddability of normal subgroups of finite groups
New criteria for hypercyclically embeddability of normal subgroups of finite groups
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DOI：
10.1007/s11587-021-00616-x
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发表时间：
2021-06
影响因子：
1.2
通讯作者：
Haoran Yu;Xiaowei Xu
中科院分区：
文献类型：
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作者：
Haoran Yu;Xiaowei Xu
根据Li和Zhao （Ukr Math J 64:102-109, 2012）的说法，一个有限群的子群称为补群，如果存在一个次正规子群tog，其中是h的Frattini子群。本文推广了补子群的概念，利用给定阶的较少的主子群给出了有限群正规子群的（p-）超环可嵌入性的若干判据。我们的主要结果不仅简化，而且推广了一些已知的关于补子群的定理。
According to Li and Zhao (Ukr Math J 64:102–109, 2012), a subgroupHof a finite groupGis said to be-supplemented inGif there exists a subnormal subgroupTofGsuch thatand, whereis the Frattini subgroup ofH. In this paper, we extend the concept of-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-supplemented subgroups.