On c#-normal subgroups of finite groups

Zhong Guo; Lin Shi-Xun

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On c#-normal subgroups of finite groups

机译：关于C＃-Normal子群的有限组

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Let H be a subgroup of a finite group G. We say that H is a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H boolean AND K is a CAP-subgroup of G. In the present paper, we use c#-normality of subgroups to characterize the structure of finite groups, and establish some necessary and sufficient conditions for a finite group to be p-supersolvable, p-nilpotent and solvable. Our results extend and improve some recent ones.

机译：设H是有限群G的子群。如果存在G的正规子群K，使得G=HK和H布尔且K是G的帽子群，我们称H是G的c#正规子群。本文利用子群的c#正规性刻画了有限群的结构，并建立了有限群p超可解的一些充要条件，p-幂零且可解。我们的结果扩展并改进了最近的一些结果。

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来源
《Journal of algebra and its applications》 |2017年第8期|共11页
作者
Zhong Guo; Lin Shi-Xun;
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作者单位

Univ Macau Fac Sci &

Technol Macau Macau SAR Peoples R China;

Zhaotong Univ Sch Math &

Stat Zhaotong 657000 Yunnan Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
c; -normal subgroups; p-supersolvable groups; p-nilpotent groups;

机译：C;- 正常亚组;对上层溶血群;P-Nilpotent组;

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2. Class-Preserving Coleman Automorphisms of Finite Groups Whose Second Maximal Subgroups Are TI-Subgroups [J] . Zhengxing LI, Jinke HAI 数学研究及应用：英文版 . 2013,第002期
3. Finite groups whose non-abelian self-centralizing subgroups are TI-subgroups or subnormal subgroups [J] . Sun Yuqing, Lu Jiakuan, Meng Wei Journal of algebra and its applications . 2021,第3期

机译：有限群体，其非雅中自集亚组是Ti-subgroups或亚因子子组
4. Finite groups in which every non-abelian subgroup is a TI-subgroup or a subnormal subgroup [J] . Shi Jiangtao Journal of algebra and its applications . 2019,第8期

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5. Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup [J] . Shi J., Zhang C. Archiv der Mathematik . 2013,第2期

机译：有限组，其中每个子组都是次普通子组或TI子组
6. Influence of Z-permutable of Maximal Subgroups of Sylow Subgroups of Finite Groups [C] . Xu Yong, Wu Dan, Zhang Xinjian 2012 Fifth International Joint Conference on Computational Sciences and Optimization . 2012

机译：有限群Sylow子群的最大子群的Z置换的影响
7. On Finitely Generated Nilpotent Groups and Their Subgroups [D] . Sandor, Bryan. 2017

机译：关于有限生成的幂等子群及其子群
8. Some subgroup embeddings in finite groups: A mini review [O] . A. Ballester-Bolinches, J.C. Beidleman, R. Esteban-Romero, 2015

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9. THE MOD 2 COHOMOLOGY ALGEBRAS OF FINITE GROUPS WITH DIHEDRAL SYLOW 2-SUBGROUPS(Representation Theory of Finite Groups and Finite Dimensional Algebras) [O] . ASAI TSUNENOBU, SASAKI HIROKI 1992

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10. Finite Unions of Closed Subgroups of the n-Dimensional Torus [R] . Lawrence, J. 1988

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On c#-normal subgroups of finite groups

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