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## The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups

#### Changwen Li [1] , Shouhong Qiao [2] , Jianhong Huang [3]

A subgroup $H$ of a group $G$ is said to be $\tau$-quasinormal in $G$ if $H$ permutes with every Sylow subgroup $Q$ of $G$ such that $(|H|,|Q|)=1$ and $(|H|,|Q|^G)\neq1$; $H$ is called partially $\tau$-quasinormal in $G$ if $G$ has a normal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $H\cap T\leq H_{\tau G}$, where $H_{\tau G}$ is the subgroup generated by all those subgroups of $H$ which are $\tau$-quasinormal in $G$. In this paper, we investigate the influence of some partially $\tau$-quasinormal subgroups on the structure
of finite group. Some new characterizations of $p$-supersoluble and $p$-nilpotent groups are obtained.

$S$-quasinormal, partially $\tau$-quasinormal, $p$-supersoluble, $p$-nilpotent
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Birincil Dil en Matematik Matematik Yazar: Changwen Li (Sorumlu Yazar) Yazar: Shouhong Qiao Yazar: Jianhong Huang Yayımlanma Tarihi : 1 Haziran 2017
 Bibtex @araştırma makalesi { hujms450969, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2017}, volume = {46}, pages = {389 - 395}, doi = {}, title = {The influence of partially \$\\tau\$-quasinormal subgroups on the structure of finite groups}, key = {cite}, author = {Li, Changwen and Qiao, Shouhong and Huang, Jianhong} } APA Li, C , Qiao, S , Huang, J . (2017). The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups. Hacettepe Journal of Mathematics and Statistics , 46 (3) , 389-395 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/38758/450969 MLA Li, C , Qiao, S , Huang, J . "The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 389-395 Chicago Li, C , Qiao, S , Huang, J . "The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 389-395 RIS TY - JOUR T1 - The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups AU - Changwen Li , Shouhong Qiao , Jianhong Huang Y1 - 2017 PY - 2017 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 389 EP - 395 VL - 46 IS - 3 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups %A Changwen Li , Shouhong Qiao , Jianhong Huang %T The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups %D 2017 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 46 %N 3 %R %U ISNAD Li, Changwen , Qiao, Shouhong , Huang, Jianhong . "The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups". Hacettepe Journal of Mathematics and Statistics 46 / 3 (Haziran 2017): 389-395 . AMA Li C , Qiao S , Huang J . The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 389-395. Vancouver Li C , Qiao S , Huang J . The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 395-389.