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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On Dehn functions and products of groups

Author: Stephen G. Brick
Journal: Trans. Amer. Math. Soc. 335 (1993), 369-384
MSC: Primary 57M20; Secondary 20E06, 20F32
MathSciNet review: 1102884
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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 HNN extensions.

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Keywords: Dehn function, isoperimetric inequality, finitely presented group, direct product, free product with amalgamation
Article copyright: © Copyright 1993 American Mathematical Society

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