关于有限群的一个组合问题

A Combinatorial Problem on Finite Groups

设ｐ是有限群Ｇ之阶ｎ的最小素因子，Ｇ之运算用“＋”来记（但不必可换），又设，本文证明了当Ｇ为幂零群及其它某些类型的群时，是满足下面条件的最小正整数：凡Ｇ的不含零元的元子集均使得Ｇ之每一个元ｇ都可表成ｇ＝ａ＿（ｉ１）＋…＋ａ＿（ｉ１），诸ｉ＿ｊ互异．

et G be a finite group of order n(Written additively),p the least prime divisor ofn,and In this paper,we prove that if G is nilpotent or G is in another certainclass ofgroups,then is the least integer t with the property that every subset a_1,…,a_t oft nonzero elements in G so that every element g∈G can be written in the form g=a_(i1)+…+a_(il),with all i_j distincted