Yıl 2017, Cilt 46 , Sayı 3, Sayfalar 389 - 395 2017-06-01

The influence 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 influence of some partially $\tau$-quasinormal subgroups on the structure
of finite group. Some new characterizations of $p$-supersoluble and $p$-nilpotent groups are obtained.

$S$-quasinormal, partially $\tau$-quasinormal, $p$-supersoluble, $p$-nilpotent
  • A. Ballester-Bolinches, L. M. Ezquerro and A. N. Skiba, Local embeddings of some families of subgroups of nite group, Acta Math. Sin. (Engl. Ser.), 25 (2009), 869882.
  • K. Doerk and T. Hawkes, Finite solvable Groups, Walter de Gruyter, Berlin-New York, 1992.
  • D. Gorenstein, Finite Groups, Harper and Row, New York, 1968.
  • B. Huppert, Endliche Gruppen I, Springer-Verlag, Berlin-New York, 1967.
  • B. Huppert and N. Blackburn, Finite Groups III, Springer-Verlag, Berlin-New York, 1982.
  • O. H. Kegel, Sylow Gruppen and subnormalteiler endlicher Gruppen, Math. Z., 78 (1962), 205221.
  • B. Li, Finite groups with $\Pi$-supplemented minimal subgroups, Commun. Algebra, 41 (2013), 20602070.
  • C. Li, X. Zhang and X. Yi, On partially $\tau$-quasinormal subgroups of finite groups, Hacet. J. Math. Stat., 43 (2014), 953961.
  • V. O. Lukyanenko and A. N. Skiba, On weakly $\tau$-quasinormal subgroups of finite groups, Acta Math. Hungar., 125 (2009), 237248.
  • P. Schmidt, Subgroups permutable with all Sylow subgroups, J. Algebra, 207 (1998), 285 293.
  • A. N. Skiba, A characterization of the hypercyclically embedded subgroups of finite groups, J. Pure Appl. Algebra, 215 (2011), 257261.
  • Y. Wang, $C$-normality and groups and its properties, J. Algebra, 180 (1996), 954965.
Birincil Dil en
Konular Matematik
Bölüm Matematik
Yazarlar

Yazar: Changwen Li (Sorumlu Yazar)

Yazar: Shouhong Qiao

Yazar: Jianhong Huang

Tarihler

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 influence 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 influence 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 influence of partially $\tau$-quasinormal subgroups on the structure of finite groups". Hacettepe Journal of Mathematics and Statistics 46 (2017 ): 389-395 <https://dergipark.org.tr/tr/pub/hujms/issue/38758/450969>
Chicago Li, C , Qiao, S , Huang, J . "The influence 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 influence 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 influence of partially $\tau$-quasinormal subgroups on the structure of finite groups %A Changwen Li , Shouhong Qiao , Jianhong Huang %T The influence 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 influence 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 influence 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 influence of partially $\tau$-quasinormal subgroups on the structure of finite groups. Hacettepe Journal of Mathematics and Statistics. 2017; 46(3): 395-389.