次正规子群与有限群的p-超可解性

Subnormal Subgroups and p-Super Solvability of Finite Groups

设群G有p-可解正规子群H且满足G/H为p-超可解群。证明:1)若H的Sylow p-子群P的极大子群在G中次正规,则G是p-超可解;2)若Op′(H)的极大子群包含于F_p(H)中且在G中次正规,则G是p-超可解群。

Let group G has solvable normal subgroup H and G/H is a p-super solvable group. Prove： 1） If the maximal subgroups of Sylow p-subgroup P of H subnormal in G, then G is a p-super solvable group; 2） If the maximal subgroups of Op, （H） include in the Fp（H） and subnormal in G, then G is a p-super solvable group.