强p-可嵌入群与极小非π-直可分群

Strongly p-embedded subgroups and minimal non-π-directly separable groups

通过对极小非π-直可分群结构的分析,利用其信号子函数的可解性,以及对于π(G)∩π′中最小素数所对应的信号子函数的完全性,文章没有应用单群的分类定理证明了极小非π-直可分群是强π-可嵌入的,其中p为π(G)∩π′中最小素数。

By analysing the structrue of a minimal non-π-directly separable group, one can define a signalizer function on a subgroup and this signalizer function is proved to be sovable and complete. Following these we finally show that this minimal non-n-directly separable group is strongly p-embedded group for the least prime p∈π（G）∩π（G） without using the Classification Theorem of Finite Simple Groups.