A note on m-embedded subgroups of finite groups

Authors: JUPING TANG, LONG MIAO

Abstract: Let $A$ be a subgroup of $G$. $A$ is m-embedded in $G$ if $G$ has a subnormal subgroup $T$ and a $\{1\leq G\}$-embedded subgroup $C$ such that $G=AT$ and $T\cap A\leq C\leq A$. In this paper, we study the structure of finite groups by using m-embedded subgroups and obtain some new results about $p$-supersolvability and $p$-nilpotency of finite groups. \vs{-1mm}

Keywords: Sylow subgroup, $\{1\leq G\}$-embedded, m-embedded subgroup, saturated formation, finite groups

Full Text: PDF