极小子群的超中心性与幂零群

Hypercenter of minimal subgroups and nilpotent group

利用完全c-可换子群的概念,得到了幂零群的2个充分条件:(1)如果群G的4阶循环子群在G中完全c-可换且G的任意极小子群含于Z∞(G)中,那么G是幂零群;(2)设N■G且G/N是幂零群.如果N的任意4阶循环子群在G中完全c-可换且N的任意极小子群包含在Z∞(G)中,那么G是幂零群.

Using the concept, completely c- permutable subgroup of finite groups, two sufficient conditions of nilpotent groups was obtained ： （ 1 ） If any cyclic subgroup of G of order 4 is completely c - permutable in G and any minimal subgroup of G is contained in the hypercenter ofG , then G is a nilpotent group. （ 2 ） Let N be a normal subgroup ofG and G/N be a nilpotent group. If any cyclic subgroup of N of order 4 is completely c-permutable in G and any minimal subgroup of N is contained in hypercenter ofG , then G is a nilpotent group.