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Solvable groups with polynomial Dehn functions

Author(s): G. N. Arzhantseva; D. V. Osin
Journal: Trans. Amer. Math. Soc. 354 (2002), 3329-3348.
MSC (2000): Primary 20F69, 20F06, 20F65, 20F16, 20F05
Posted: April 3, 2002
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Abstract: Given a finitely presented group $H$, finitely generated subgroup $B$ of $H$, 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 $H$ and the distortion of $B$ in $G$. 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.

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Additional Information:

G. N. Arzhantseva
Affiliation: Section de Mathématiques, Université de Genève, CP 240, 1211 Genève 24, Switzerland
Email: Goulnara.Arjantseva@math.unige.ch

D. V. Osin
Affiliation: Department of High Algebra, MEHMAT, Moscow State University, 119899 Moscow, Russia
Email: Denis.Osin@mtu-net.ru

DOI: 10.1090/S0002-9947-02-02985-9
PII: S 0002-9947(02)02985-9
Keywords: Dehn function, isoperimetric function, HNN-extension, van Kampen diagram, metabelian group
Received by editor(s): August 2, 2000
Received by editor(s) in revised form: October 13, 2000
Posted: April 3, 2002
Additional Notes: The work has been supported by the Swiss National Science Foundation
Copyright of article: Copyright 2002, American Mathematical Society

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