@article { author = {Mao, Y. and Ma, X. and Tang, X. and Huang, J.}, title = {On $\Phi$-$\tau$-quasinormal subgroups of finite groups}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {43}, number = {7}, pages = {2169-2182}, year = {2017}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {‎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.}, keywords = {$S$-quasinormal subgroups,$p$-nilpotent subgroups‎, ‎subgroup functor,soluble group‎}, url = {http://bims.iranjournals.ir/article_1088.html}, eprint = {http://bims.iranjournals.ir/article_1088_42c83e5c0a23d661fa95aaa1ad32dcfa.pdf} }