This article is cited in 8 papers

On primitive representations of soluble groups of finite rank

A. V. Tushev

Dnepropetrovsk State University

Abstract: In the paper it is proved, in particular, that a group is polycyclic if and only if it is soluble of finite rank, satisfies the ascending chain condition for normal subgroups and admits a faithful irreducible primitive representation over a field of characteristic zero. Methods are developed that enable one to study induced representations of nilpotent and soluble groups of finite rank.

UDC: 512.544

MSC: Primary 20C07, 16S34; Secondary 16P40, 20F16, 20F18

Received: 04.11.1999

DOI: 10.4213/sm524

 English version: Sbornik: Mathematics, 2000, 191:11, 1707–1748

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