On Dehn functions and products of groups

Abstract

If G G is a finitely presented group then its Dehn function—or its isoperimetric inequality—is of interest. For example, G G satisfies a linear isoperimetric inequality iff G G is negatively curved (or hyperbolic in the sense of Gromov). Also, if G G possesses an automatic structure then G G satisfies a quadratic isoperimetric inequality. We investigate the effect of certain natural operations on the Dehn function. We consider direct products, taking subgroups of finite index, free products, amalgamations, and HNN \text {HNN} extensions.