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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Solvable groups with polynomial Dehn functions
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by G. N. Arzhantseva and D. V. Osin PDF
Trans. Amer. Math. Soc. 354 (2002), 3329-3348 Request permission


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 $G=\langle H, t\; |\; t^{-1}Bt=\psi (B)\rangle$ 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:
  • D. V. Osin
  • Affiliation: Department of High Algebra, MEHMAT, Moscow State University, 119899 Moscow, Russia
  • MR Author ID: 649248
  • Email:
  • Received by editor(s): August 2, 2000
  • Received by editor(s) in revised form: October 13, 2000
  • Published electronically: April 3, 2002
  • Additional Notes: The work has been supported by the Swiss National Science Foundation
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 3329-3348
  • MSC (2000): Primary 20F69, 20F06, 20F65, 20F16, 20F05
  • DOI:
  • MathSciNet review: 1897402