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The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups

Year 2017, Volume: 46 Issue: 3, 389 - 395, 01.06.2017

Abstract

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.

References

  • 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.
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  • 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.
Year 2017, Volume: 46 Issue: 3, 389 - 395, 01.06.2017

Abstract

References

  • 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.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Changwen Li This is me

Shouhong Qiao This is me

Jianhong Huang This is me

Publication Date June 1, 2017
Published in Issue Year 2017 Volume: 46 Issue: 3

Cite

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.
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. June 2017;46(3):389-395.
Chicago Li, Changwen, Shouhong Qiao, and Jianhong Huang. “The influence of Partially $\tau$-Quasinormal Subgroups on the Structure of finite Groups”. Hacettepe Journal of Mathematics and Statistics 46, no. 3 (June 2017): 389-95.
EndNote Li C, Qiao S, Huang J (June 1, 2017) The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups. Hacettepe Journal of Mathematics and Statistics 46 3 389–395.
IEEE C. Li, S. Qiao, and J. Huang, “The influence of partially $\tau$-quasinormal subgroups on the structure of finite groups”, Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, pp. 389–395, 2017.
ISNAD Li, Changwen et al. “The influence of Partially $\tau$-Quasinormal Subgroups on the Structure of finite Groups”. Hacettepe Journal of Mathematics and Statistics 46/3 (June 2017), 389-395.
JAMA 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;46:389–395.
MLA Li, Changwen et al. “The influence of Partially $\tau$-Quasinormal Subgroups on the Structure of finite Groups”. Hacettepe Journal of Mathematics and Statistics, vol. 46, no. 3, 2017, pp. 389-95.
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):389-95.