Isoperimetric functions for graph products

Abstract

Let Γ 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 EG i and h G j and there is an edge joining i and j. We show that G has an isoperimetric function of degree k > 1 (or an exponential isoperimetric function) if each vertex group has such an isoperimetric function.