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 language | English |
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Pages (from-to) | 189-198 |
Number of pages | 10 |
Journal | Journal of Pure and Applied Algebra |
Volume | 90 |
Issue number | 2 |
DOIs | |
State | Published - 1 Dec 1993 |