On Dehn functions and products of groups

Brick, Stephen G.

doi:10.1090/S0002-9947-1993-1102884-1

On Dehn functions and products of groups
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by Stephen G. Brick

Trans. Amer. Math. Soc. 335 (1993), 369-384

DOI: https://doi.org/10.1090/S0002-9947-1993-1102884-1

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Abstract:

If $G$ is a finitely presented group then its Dehn function—or its isoperimetric inequality—is of interest. For example, $G$ satisfies a linear isoperimetric inequality iff $G$ is negatively curved (or hyperbolic in the sense of Gromov). Also, if $G$ possesses an automatic structure then $G$ 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 $\text {HNN}$ extensions.

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