关键词: 基, 有限群, 基数

Abstract: Let G be a multiplicative group, B be a subset of G and h>=2 be an integer. Denote by B^h the set of all products of h elements of B . The set B is a basis of order h for G if B^h=G . In this paper the following result is proved: if G is a finite group of order n, then there exists a subset B of Gsuch that B^h=G and ｜B｜<= h(1- 1／ h )^1／h(n ·log n)^1／h+o(n^1／h) , where｜B｜is the cardinality of the subset B .

Key words: basis, finite group, cardinality