Isoperimetric functions for graph products

Details Isoperimetric functions for graph products Isoperimetric functions for graph products

1993-10-16

arxiv.org/abs/math/9310208v1

Mathematics

Group Theory

AMS-Tex, 5 pages, no figures

Scientific paper

Let $\Gamma$ be a finite graph, and for each vertex $i$ let $G_i$ be a finitely presented group. Let $G$ be the graph product of the $G_i$. That is, $G$ is the group obtained from the free product of the $G_i$ by factoring out by the smallest normal subgroup containing all $[g,h]$ where $g\in G_i$ and $h\in G_j$ and there is an edge joining i and j . We show that $G$ has an isoperimetric function of degree $k\ge 2$ (or an exponential isoperimetric function) if each vertex group has such an isoperimetric function.

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