次正规嵌入子群与有限群的可解性(Ⅰ)

Subnormally Embedded Subgroups and Solvability of Finite Groups

证明了,设P是群G的Sylow 2-子群,若P的极大子群都在G中次正规嵌入,则G可解;若群G的Sylow 2-子群的循环子群均在G中次正规嵌入,则G可解;设M为群G的幂零极大子群或M为群G的内2-幂零极大子群,若M的Sylow 2-子群的极大子群都在G中次正规嵌入,则G可解.

Let P be a Sylow 2-subgroup of a group G I.f the maximal subgroup of P is subnormal-ly embedded in G ,then G is solvable I.f a cyclic subgroup of Sylow 2-subgroup of a group G is subnor-mally embedded in G .then G is solvable .Let M be a nilpotnent maximal subgroup of a group G or M be an inner 2-nilpotent maximal subgroup of a group G ,if the maximal subgroup of Sylow 2-subgroup of M is subnormally embedded in G ,then G is solvable .