具有弱$s$-置换嵌入子群的有限群

Let P be a Sylow p-subgroup of a group G with the smallest generator number d,where p is a prime.Denote by M_d(P) = {P_1,P_(2,...,)P_d} a set of maximal subgroups of P such that φ(P) = ∩_(n=1)~dP_n.In this paper,we investigate the structure of a finite group G under the assumption that the maximal subgroups in M_d(P) are weakly s-permutably embedded in G,some interesting results are obtained which generalize some recent results.Finally,we give some further results in terms of weakly s-permutably embedded subgroups.

Finite Groups with Some Subgroups Weakly $s$-Permutably Embedded

Let $P$ be a Sylow $p$-subgroup of a group $G$ with the smallest generator number $d$, where $p$ is a prime. Denote by $\cal M$$_d(P)=\{P_1,P_2,\ldots,P_d\}$ a set of maximal subgroups of $P$ such that $\Phi(P)=\cap^{d}_{n=1}P_n$. In this paper, we investigate the structure of a finite group $G$ under the assumption that the maximal subgroups in $\cal M$$_d(P)$ are weakly $s$-permutably embedded in $G$, some interesting results are obtained which generalize some recent results. Finally, we give some further results in terms of weakly $s$-permutably embedded subgroups.