Primitive and measure-preserving systems of elements on the varieties of metabelian and metabelian profinite groups

被引：4

作者：

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

机构：

[1] Novosibirsk State Tech Univ, Novosibirsk, Russia

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2013年 / 54卷 / 01期

基金：

俄罗斯基础研究基金会;

关键词：

primitive system of elements; measure-preserving system of elements; metabelian group; profinite group;

D O I：

10.1134/S0037446613010199

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a free metabelian group S of finite rank r, r >= 2, we prove that a system of elements g (1), ..., g (n) is an element of S for n = 1 or n = r preserves measure on the variety of all metabelian groups if and only if the system is primitive. Similar results hold for a free profinite group (S) over cap and the variety of finite metabelian groups for each n, 1 <= n <= r. Some corollaries to these theorems are derived.

引用

页码：152 / 158

页数：7