Just infinite modules over metabelian groups of finite rank

A. V. Tushev

Dnepropetrovsk State University

Abstract: It is proved, in particular, that if $G$ is a metabelian group of finite rank and $M$ is a faithful just infinite $\mathbb ZG$-module, then $G$ is finitely generated. This includes studying properties of induced modules over the group algebra $kG$ of a metabelian group $G$ of finite rank over a field $k$ of arbitrary characteristic.

UDC: 512.544

MSC: Primary 20C07, 16S34; Secondary 16P40, 20F16

Received: 21.05.2001

DOI: 10.4213/sm655

 English version: Sbornik: Mathematics, 2002, 193:5, 761–778

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