Localized theorems of finite groups with <inline-formula><tex-math id="M725">\begin{document}$\mathcal{M}_p$\end{document}</tex-math></inline-formula>-supplemented subgroups

BAO Hong-wei; LI Feng-qing; ZHANG Jia; TANG Ju-ping

doi:10.3969/j.issn.1000-5641.2019.02.007

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BAO Hong-wei, LI Feng-qing, ZHANG Jia, TANG Ju-ping. Localized theorems of finite groups with $\mathcal{M}_p$-supplemented subgroups[J]. Journal of East China Normal University (Natural Sciences), 2019, (2): 63-68. doi: 10.3969/j.issn.1000-5641.2019.02.007

Citation:

BAO Hong-wei, LI Feng-qing, ZHANG Jia, TANG Ju-ping. Localized theorems of finite groups with $\mathcal{M}_p$-supplemented subgroups[J]. Journal of East China Normal University (Natural Sciences), 2019, (2): 63-68. doi: 10.3969/j.issn.1000-5641.2019.02.007

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Localized theorems of finite groups with $\mathcal{M}_p$-supplemented subgroups

doi: 10.3969/j.issn.1000-5641.2019.02.007

1.
Faculty of Science, Bengbu University, Bengbu Anhui 233030, China
2.
Sichuan Vocational and Technical College, Suining Sichuan 629000, China
3.
School of Mathematics and Information, China West Normal University, Nanchong Sichuan 637009, China
4.
Wuxi Institute of Technology, Wuxi Jiangsu 214121, China

Received Date: 2018-02-02
Publish Date: 2019-03-25

Abstract

Abstract

A subgroup $H$ of $G$ is $\mathcal{M}_p$-supplemented in $G$, if there exists a subgroup $B$ of $G$ such that $G=HB$ and $TB < G$ for every maximal subgroup $T$ of $H$ with $|H:T|=p^\alpha$. Based on the idea of localization, by using the $\mathcal{M}_p$-supplemented properties of some primary subgroups to study the structure of finite groups, we obtained sufficient conditions for $p$-nilpotent and $p$-supersolvable groups.

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References(9)

References

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