论文标题
在$ c $ - 填充有限组的子群体
On $c$-embedded subgroups of finite groups
论文作者
论文摘要
让$ g $为一个组，$ h \ le k \ le g $。我们说，如果有$ k $，则$ h $是$ g $的$ c $，如果有$ g $ $ g $的$ k $，则$ g = hb $和$ h \ cap b \ le le z（k）$。给定有限的集团$ g $，质量$ p $和sylow $ p $ -subgroup $ p $ $ g $，我们在假设$ n_g（p）$是$ n_g（p）$是$ p $ -supersolvable或$ p $ -nillpotent and $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $的假设下，调查$ g $的结构。 $ P $。将获得$ p $ -supersolability的新特征和有限组的$ p $ nilpotence。
Let $G$ be a group and $H \le K \le G$. We say that $H$ is $c$-embedded in $G$ with respect to $K$ if there is a subgroup $B$ of $G$ such that $G = HB$ and $H \cap B \le Z(K)$. Given a finite group $G$, a prime number $p$ and a Sylow $p$-subgroup $P$ of $G$, we investigate the structure of $G$ under the assumption that $N_G(P)$ is $p$-supersolvable or $p$-nilpotent and that certain cyclic subgroups of $P$ with order $p$ or $4$ are $c$-embedded in $G$ with respect to $P$. New characterizations of $p$-supersolvability and $p$-nilpotence of finite groups will be obtained.
