TY - JOUR ID - 1088 TI - On $\Phi$-$\tau$-quasinormal subgroups of finite groups JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Mao, Y. AU - Ma, X. AU - Tang, X. AU - Huang, J. AD - Institute of Quantum Information Science‎, ‎Shanxi Datong University‎ ‎Datong 037009‎, ‎P.R‎. ‎China. AD - School of Mathematics and Computer‎, ‎University of Datong of Shanxi‎, ‎Datong 037009‎, ‎P.R‎. ‎China. AD - School of Mathematical Sciences‎, ‎University of Science and Technology of China‎, ‎Hefei‎, ‎230026‎, ‎P.R‎. ‎China. AD - School of mathematics and statistics‎, ‎Jiangsu Normal University‎ ‎Xuzhou‎, ‎221116‎, ‎P.R‎. ‎China. Y1 - 2017 PY - 2017 VL - 43 IS - 7 SP - 2169 EP - 2182 KW - $S$-quasinormal subgroups KW - $p$-nilpotent subgroups‎, ‎subgroup functor KW - soluble group‎ DO - N2 - ‎Let $\tau$ be a subgroup functor and $H$ a $p$-subgroup of a finite group $G$‎. ‎Let $\bar{G}=G/H_{G}$ and $\bar{H}=H/H_{G}$‎. ‎We say that $H$ is $\Phi$-$\tau$-quasinormal in $G$ if for some $S$-quasinormal subgroup $\bar{T}$ of $\bar{G}$ and some $\tau$-subgroup $\bar{S}$ of $\bar{G}$ contained in $\bar{H}$‎, ‎$\bar{H}\bar{T}$ is $S$-quasinormal in $\bar{G}$ and $\bar{H}\cap\bar{T}\leq \bar{S}\Phi(\bar{H})$‎. ‎In this paper‎, ‎we study the structure of a group $G$ under the condition that some primary subgroups of $G$ are $\Phi$-$\tau$-quasinormal in $G$‎. ‎Some new characterizations about $p$-nilpotency and solubility of finite groups are obtained. UR - http://bims.iranjournals.ir/article_1088.html L1 - http://bims.iranjournals.ir/article_1088_42c83e5c0a23d661fa95aaa1ad32dcfa.pdf ER -