FINITELY GENERATED SOLUBLE GROUPS WITH A CONDITION ON INFINITE SUBSETS

被引：1

作者：

Salles, Asadollah Faramarzi ^{[1
]}

机构：

[1] Damghan Univ, Dept Math, Damghan, Iran

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2013年 / 87卷 / 01期

关键词：

finitely generated groups; nilpotent groups; soluble groups;

D O I：

10.1017/S0004972712000457

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a group. We say that G is an element of T (infinity) provided that every infinite set of elements of G contains three distinct elements x, y, z such that x not equal y; [x, y, z] = 1 = [y, z, x] = [z, x, y]. We use this to show that for a finitely generated soluble group G, G/Z(2)(G) is finite if and only if G is an element of T (infinity).

引用

页码：152 / 157

页数：6

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