Solvable groups with cyclic relation module

Jens Harlander

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

If P is a group of operators on a group A, then we denote by dP(A) the minimal number of generatorsof A as a P-group. Suppose G is a group and F/N is a presentation of G. Then F acts on N by conjugation and induces an action of G on Nab. This ZG-module is called the relation module of the presentation F/N. A presentation F/N is an m-relator presentation if dF(N) = m; it is an almost m-relator presentation if dG(Nab) = m. It is an open problem whether every almost m-relator presentation is an m-relator presentation. This paper is part of a program to investigate this question when m = 1. We show that an almost one-relator presentation F/N is a one-relator presentation in case the group G = F/N is finitely generated and solvable.

Original languageEnglish
Pages (from-to)189-198
Number of pages10
JournalJournal of Pure and Applied Algebra
Volume90
Issue number2
DOIs
StatePublished - 1 Dec 1993

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