p-可分群的两个充分条件

Two sufficient conditions of p-decomposable groups

φ表示p-可分群的群类.利用c-补子群的概念,得到了p-可分群的两个充分条件:(1)如果群G的4阶循环子群在G中c-可补且G的任意极小子群含于G的φ-超中心Zφ(G)中,那么G是p-可分群;(2)设HG且G/H是p-可分群.如果H的任意4阶循环子群在G中c-可补且H的任意极小子群包含在G的φ-超中心Zφ(G)中,那么G是p-可分群.

Let φ be the class of all p-decomposable groups. Using the concept, c-supplement of subgroup, two sufficient conditions of p-decomposable groups are obtained ： （ 1 ） If any cyclic subgroup of G of order 4 is c-suplemented in G and any minimal subgroup of G is contained in φ-hypercenter of G,then G is a p-decomposable group; （2）Let H be a normal subgroup of G and G/H be a p-decomposable group. If any cyclic subgroup of H of order 4 is c-supplemented in G and any minimal subgroup of H is contained in φ-hypercenter of G, then G is a p-decomposable group.