Finite group with Hall normally embedded minimal subgroups
Let G be a finite group. A subgroup H of G is called Hall normally embedded in G if H is a Hall subgroup of H (Formula presented.), where H (Formula presented.) is the normal closure of H in G, that is, the smallest normal subgroup of G containing H. A group G is called an HNE -group if all cyclic subgroups of order 2 and 4 of G are Hall normally embedded in G. In this paper, we prove that all HNE -groups are 2-nilpotent. Furthermore, we also characterize the structure of finite group all of whose maximal subgroups are HNE -groups. Finally, we determine finite non-solvable groups all of whose second maximal subgroups are HNE -groups.
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|Document Type||Journal Article|
|Department||SUSTech International Center for Mathematics|
1.School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin,Guangxi,China
2.SUSTech International Center for Mathematics,Shenzhen,Guangdong,China
3.School of Mathematics and Statistics,Guangxi Normal University,Guilin,Guangxi,China
|Corresponding Author Affilication||SUSTech International Center for Mathematics|
Cui，Liang,Zheng，Weicheng,Meng，Wei,et al. Finite group with Hall normally embedded minimal subgroups[J]. Communications in Algebra,2023.
Cui，Liang,Zheng，Weicheng,Meng，Wei,&Lu，Jiakuan.(2023).Finite group with Hall normally embedded minimal subgroups.Communications in Algebra.
Cui，Liang,et al."Finite group with Hall normally embedded minimal subgroups".Communications in Algebra (2023).
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