摘要
本文给出可分解群为y-群的几个充分条件,主要结果为: 定理1 设G=AB,AG,BG,A,B是δy群,若下列之一条件满足 1)(|G:A|,|G:B|)=1,且G不含截断W_1 2)(|A|,|B|)=1则G为y-群。 定理2 设G=AB=AC=BC,A,B,C是δy群,且|G:A|,|G:B|,|G:C|两两互素,则G为y-群。 定理3 设G=AB,A,B是δy群,|G:A|=p,|G:B|=q,其中p为|G|的最小素因子,q为|G|的最大素因子,如果G不含截断W,则G为y-群。
In this note, Some sufficient conitions factorable groups are y-groups are given, the main results are as follows,Theorem 1 Let G =AB, Where A and B are normal δy subgroups. If one of the following conditions1 ) ( |G : | | , |G = B | )= |and G is section W1-free.2) (|A|, |B|) =1 is satisfied , then G is a y-group.Theorem 2 Let G = AB = AC = BC , Where A , B and C are δy subgroups of relatively prime index in G, then G is a y-group.Theorem 3 Let G = AB, A and B are δy subgroups of G, |G : A|=p, |G : B|=q, p is a minmal prime factor of |G| , q is a maxmal prime factor of |G|. If G is section W-free, then G is a y-group.
出处
《山西师大学报（自然科学版）》
1995年第4期15-18,共4页
Journal of Shanxi Teachers University(Natural Science Edition)
