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Solvable groups with polynomial Dehn functions

Authors:	G N Arzhantseva D V Osin

Institution:	Section de Mathématiques, Université de Genève, CP 240, 1211 Genève 24, Switzerland ; Department of High Algebra, MEHMAT, Moscow State University, 119899 Moscow, Russia

Abstract:	Given a finitely presented group , finitely generated subgroup of , and a monomorphism $\psi :B\to H$ , we obtain an upper bound of the Dehn function of the corresponding HNN-extension $G=\langle H, t \vert t^{-1}Bt=\psi (B)\rangle$ in terms of the Dehn function of and the distortion of in . Using such a bound, we construct first examples of non-polycyclic solvable groups with polynomial Dehn functions. The constructed groups are metabelian and contain the solvable Baumslag-Solitar groups. In particular, this answers a question posed by Birget, Ol'shanskii, Rips, and Sapir.

Keywords:	Dehn function isoperimetric function HNN-extension van Kampen diagram metabelian group

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