次正规嵌入子群与有限群的p-超可解性

Subnormal Embedded Subgroups and p-super Solvability of Finite Groups

设H是群G的p-可解正规子群使得G/H为p-超可解.1)若H的Sylowp-子群P的极大子群皆在G中次正规嵌入,则G是p-超可解群;2)若F_p(H)包含O_(p′)(H)的极大子群都在G中次正规嵌入,则G是p-超可解群.

Suppose H is p - solvable normal subgroup in G such that G/H is p - super solvable group. 1）If a maximal subgroup of Sylow p-subgroup P of H is subnormal embedded in G,then G is p- super solvable group;2）If a maximal subgroup of Fp（H） which involves Op, （H） is subnormal embedded in G, then G is p -super solvable group.