Acta Scientiarum Naturalium Universitatis Pekinensis

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On Bases of Finite Groups

CHEN Yonggao   

  1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097
  • Received:1995-08-10 Online:1996-09-20 Published:1996-09-20



  1. 南京师范大学数学系,南京,210097

Abstract: Let G be a multiplicative group, B be a subset of G and h>=2 be an integer. Denote by Bh the set of all products of h elements of B . The set B is a basis of order h for G if Bh=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 Bh=G and |B|<= h(1- 1/ h )1/h(n ·log n)1/h+o(n1/h) , where|B|is the cardinality of the subset B .

Key words: basis, finite group, cardinality

摘要: 设G为乘法群,B为G的子集,h为不小于2的整数,Bh为B中h各元素之积所成的集合。若Bh=G,则称B为G的阶为h的基。本文证明了如下结论:若G为n阶群,则存在G的子集B,使得Bh=G,|B|≤h(1-(1/h))1/h(nlogn)1/h+o(n)1/h),其中|B|为子集B的基数。

关键词: 基, 有限群, 基数

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