Generation Gaps and Abelianised Defects of Free Products
| dc.creator | Gruenberg, Karl W. | |
| dc.creator | Linnell, Peter A. | |
| dc.date | 2007-01-08 | |
| dc.date | 2007-12-26 | |
| dc.date.accessioned | 2026-07-07T08:51:01Z | |
| dc.date.available | 2026-07-07T08:51:01Z | |
| dc.description | Let G be a group of the form G_1* ... *G_n, the free product of n subgroups, and let M be a ZG-module of the form $\bigoplus_{i=1}^n M_i \otimes_{\mathbb{Z}G_i} \mathbb{Z}G$. We shall give formulae in various situations for $d_{ZG}(M)$, the minimum number of elements required to generate M. In particular if C_1,C_2 are non-trivial finite cyclic groups of coprime orders, $G = (C_1 \times Z) * (C_2 \times Z)$ and $F/R \cong G$ is the free presentation obtained from the natural free presentations of the two factors, then the number of generators of the relation module, $d_{\mathbb{Z}G}(R/R')$ is three. It seems plausible that the minimum number of relators of G should be 4, and this would give a finitely presented group with positive relation gap. However we cannot prove this last statement. | |
| dc.description | 18 pages, minor changes. To appear in J. Group Theory | |
| dc.identifier | https://arxiv.org/abs/math/0701225 | |
| dc.identifier | http://arxiv.org/abs/math/0701225 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144797 | |
| dc.subject | Group Theory | |
| dc.subject | 20F05 (Primary) 20E06 (Secondary) | |
| dc.title | Generation Gaps and Abelianised Defects of Free Products | |
| dc.type | text |