On weakly <i>s</i> -normal subgroups of finite groups

  • Yangming Li Guangdong Univ. Education, China
  • Shouhong Qiao Yunnan Univ., Kunming, China


Assume that $G$ is a finite group and $H$ is a subgroup of $G$. We say that $H$ is $s$-permutably imbedded in $G$ if, for every prime number p that divides $|H|$, a Sylow $p$-subgroup of $H$ is also a Sylow $p$-subgroup of some $s$-permutable subgroup of $G$; a subgroup $H$ is $s$-semipermutable in $G$ if $HG_p = G_pH$ for any Sylow $p$-subgroup $G_p$ of $G$ with $(p, |H|) = 1$; a subgroup $H$ is weakly $s$-normal in $G$ if there are a subnormal subgroup $T$ of $G$ and a subgroup $H_{*}$ of $H$ such that $G = HT$ and $H \bigcap T ≤ H_{*}$, where $H_{*}$ is a subgroup of $H$ that is either $s$-permutably imbedded or $s$-semipermutable in $G$. We investigate the influence of weakly $s$-normal subgroups on the structure of finite groups. Some recent results are generalized and unified.
How to Cite
Li, Y., and S. Qiao. “On Weakly <i>s</I&gt; -Normal Subgroups of Finite Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 11, Nov. 2011, pp. 1555-64, https://umj.imath.kiev.ua/index.php/umj/article/view/2825.
Research articles