Conditions for $p$-supersolubility and $p$-nilpotency of finite soluble groups

Volume 133 / 2013

Wenai Yan, Baojun Li, Zhirang Zhang Colloquium Mathematicum 133 (2013), 85-98 MSC: 20D10, 20D20. DOI: 10.4064/cm133-1-6

Abstract

Let $\mathfrak {Z}$ be a complete set of Sylow subgroups of a group $G$. A subgroup $H$ of $G$ is called $\mathfrak {Z}$-permutably embedded in $G$ if every Sylow subgroup of $H$ is also a Sylow subgroup of some $\mathfrak {Z}$-permutable subgroup of $G$. By using this concept, we obtain some new criteria of $p$-supersolubility and $p$-nilpotency of a finite group.

Authors

  • Wenai YanCollege of Mathematics
    Chengdu University of Information Technology
    Chengdu 610225, P.R. China
  • Baojun LiCollege of Mathematics
    Chengdu University of Information Technology
    Chengdu 610225, P.R.China
    e-mail
  • Zhirang ZhangCollege of Mathematics
    Chengdu University of Information Technology
    Chengdu 610225, P.R.China

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