Z. Shen, J. Zhang, G. Chen, Y. Chen, “On <nobr>$S$</nobr>-Quasinormally Embedded Subgroups of Finite Groups”, Mat. Zametki, 2017, Volume 101, Issue 4,Pages <nobr>735

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Papers published in the English version of the journal

On $S$-Quasinormally Embedded Subgroups of Finite Groups

Z. Shen^a, J. Zhang^b, G. Chen^c, Y. Chen^d

^a School of Science, Sichuan University of Science and Engineering, Zigong, China
^b Department of Mathematics of College of Science, China Agricultural University, Beijing, China
^c Shandong Water Polytechnic, Rizhao, China
^d College of Information and Electrical Engineering, China Agricultural University, Beijing, China

Abstract: A subgroup $H$ of a group $G$ is said to be $S$-quasinormally embedded in $G$ if for every Sylow subgroup $P$ of $H$, there is an $S$-quasinormal subgroup $K$ in $G$ such that $P$ is also a Sylow subgroup of $K$. Groups with certain $S$-quasinormally embedded subgroups of prime power order are studied. We prove Theorems 1.4, 1.5 and 1.6 of [10] remain valid if we omit the assumption that $G$ is a group of odd order.

Keywords: $S$-quasinormally embedded subgroups; $p$-nilpotent group; supersolvable group; formation.

Language: English