摘要
设Sri(i=1,2,…,n)为秩ri的自由亚交换群,G=Sr1×Sr2…×Srn为自由亚交换群的直积,本文证明了G有检验元素的充分必要条件为ri=2(i=1,2,…,n).同时,还证明了g=(g1,g2,…,gn)为G的检验元素的充分必要条件是:gi∈S′2-1(i= 1,2,…,n),且{g1,g2,…,gn}为独立集.此外,我们给出了一类具体的检验元素.
Let Sri, (i = 1,2,... ,n) be free metabelian groups of rank ri, G = Sr1 × Sr2 × ... × Srn be direct product of free metabelian groups. In this paper, we prove that G has test element if and only if ri = 2 (i = 1,2,... ,n). Meanwhile, we prove that g = (g1, g2,..., gn) is a test element of G if and only if gi ∈ S2^′ - 1 (i = 1, 2,..., n), and {g1,g2,..,gn} is an independent set.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2006年第4期803-808,共6页
Acta Mathematica Sinica:Chinese Series
基金
云南大学基金资助重点项目(2004Z010C)