关于群的方次数的若干结果

Some results of the exponent of a group

群的方次数是群论中的一个基本概念,它反映了群的元素阶的性质特征.通过对群的方次数的初步探讨,得到结论:若群G的元素阶均有限,且sup|a|a∈G=sup|a|a∈C(G),则群G的方次数expG=sup|a|a∈C(G).并进一步用方次数刻划了群的结构.

The exponent of a group is a basic conception of group theory, which indicates the property character of orders of elements of a group. This paper makes primary research into the exponent of group,and has the conclusion as following. Let the orders of elements of group G are finite, and sup｜a｜a∈G=sup｜a｜a∈C｜G｜, then, the exponent of G expG=sup｜a｜a∈C｜G｜Moreover, the structure of the group is represented with exponent further.