This article is cited in 3 papers

Influence of $\mathscr M_p$-supplemented subgroups on the structure of $p$-modular subgroups

B. Gao^a, L. Miao^b, J. Tang<sup>c

a</sup> School of Mathematics and Statistics, Yili Normal University, Yining, People's Republic of China
^b School of Mathematical Sciences, Yangzhou University, Yangzhou, People's Republic of China
^c Wuxi Institute of Technology, Wuxi, People's Republic of China

Abstract: A subgroup $K$ of $G$ is $\mathscr M_p$-supplemented in $G$ if there exists a subgroup $B$ of $G$ such that $G=KB$ and $TB<G$ for every maximal subgroup $T$ of $K$ with $|K:T|=p^\alpha$. We study the structure of the chief factor of $G$ by using $\mathscr M_p$-supplemented subgroups and generalize the results of Monakhov and Shnyparkov by involving the relevant results about the $p$-modular subgroup $O^p(G)$ of $G$.

Keywords: $\mathscr M_p$-supplemented subgroup, Sylow subgroup, chief factor, $p$-supersolvability.

UDC: 512.542

MSC: 20D10, 20D20

Received: 16.07.2016

DOI: 10.17377/smzh.2017.58.406

 English version: Siberian Mathematical Journal, 2017, 58:4, 606–610

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