【摘要】 从某一特殊的子群出发研究原群的结构是有限群论研究的一种重要方法。有限群G分解为子群A与B之积,即G=AB,子群A和B的构造对群G有怎样的影响是一个活跃的研究课题。1958年由H.Wielandt已证明了,若G满足G=AB,且A,B是G的有限幂零群,则G为可解群。文章将进一步讨论满足该条件的群G的性质,并得出了满足该条件的群G幂零的两个充分条件。更多还原

【Abstract】 It is an important way of getting the properties and the instructions of the group G from the properties of the special subgroups of G. If a finite group G ,A,B are subgroups and G=AB, It is an activity subject to get the properties of the group G from the properties of the special subgroups of G. In 1958 H.Wielandt got a result :if a finite Group G ,A,B are nilpotent subgroups and G=AB,so G is soluble. In this paper,we research the properties of the product of two nilpotent subgroups and we get two sufficient conditions for the nilpotency of the product of two nilpotent subgroups.更多还原