Quasivarieties generated by partially commutative groups

被引：3

作者：

Timoshenko, E. I. ^{[1
]}

机构：

[1] Novosibirsk State Tech Univ, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2013年 / 54卷 / 04期

基金：

俄罗斯基础研究基金会;

关键词：

quasivariety; prevariety; partially commutative group; metabelian group; graph; CENTRALIZER DIMENSION;

D O I：

10.1134/S0037446613040125

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a partially commutative metabelian group is a subgroup in a direct product of torsion-free abelian groups and metabelian products of torsion-free abelian groups. From this we deduce that all partially commutative metabelian (nonabelian) groups generate the same quasivariety and prevariety. On the contrary, there exists an infinite chain of different quasivarieties generated by partially commutative groups with defining graphs of diameter 2.

引用

页码：722 / 730

页数：9

共 13 条

[1] Algebraic geometry over groups I. Algebraic sets and ideal theory [J].