On s-semipermutable or s-quasinormally Embedded Subgroups of Finite Groups

Kong, Qingjun ; Guo, Xiuyun

Canadian mathematical bulletin, Tome 58 (2015) no. 4, pp. 799-807

Résumé

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$ . $H$ is said to be $s$ -semipermutable in $G$ if $H{{G}_{p}}\,=\,{{G}_{p}}H$ for any Sylow $p$ -subgroup ${{G}_{p}}$ of $G$ with $\left( p,\,\left| H \right| \right)\,=\,1$ ; $H$ is said to be $s$ -quasinormally embedded in $G$ if for each prime $p$ dividing the order of $H$ , a Sylow $p$ -subgroup of $H$ is also a Sylow $p$ -subgroup of some $s$ -quasinormal subgroup of $G$ . In every non-cyclic Sylow subgroup $P$ of $G$ we fix some subgroup $D$ satisfying $1\,<\,\left| D \right|\,<\,\left| P \right|$ and study the structure of $G$ under the assumption that every subgroup $H$ of $P$ with $\left| H \right|\,=\,\left| D \right|$ is either $s$ -semipermutable or $s$ -quasinormally embedded in $G$ . Some recent results are generalized and unified.

Détail

DOI : 10.4153/CMB-2014-073-1

Mots-clés : 20D10, 20D20, s-semipermutable subgroup, s-quasinormally embedded subgroup, saturated formation