一类有限群子群的正规化子升链

运用群在集合上作用的方法,给出Pⁿq阶群G某些子群的正规化子升链有限步终止于自身的若干条件.由这些条件得到阶为Pnq阶群G某些子群的正规化子升链有限步终止于自身的若干条件.由这些条件得到阶为Pⁿq或Pnq或Pⁿqnq^m(m>1)的群G的一些性质判别条件.证明了pm(m>1)的群G的一些性质判别条件.证明了pⁿq(q>Pnq(q>P^(n-1))阶群G的子群H的正规化子升链的末项是G的真子群时,升链的末项必在G中M-可补.

The ascending chain for normalizer of the subgroups of a class of finite groups

By using the methods of groups acting on sets, gave some conditions about the ascending chains for normalizer of some subgroups ofpnq order groups G end at the group itself in finite steps. Some criteria for judging the properties of p＂q or p＂q＂ （m 〉 1） order groups can be obtained by the above conditions. Finally, proved that the last term of the ascending chain for normalizer of the subgroup H in group G is M - supplemented in G under assumption that the last term of the ascending chain is a proper subgroup ofpnq order groups G.