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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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Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families
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by D. Groves and M. Hull PDF
Trans. Amer. Math. Soc. 372 (2019), 7141-7190 Request permission


We study the set of homomorphisms from a fixed finitely generated group $G$ into a family of groups $\mathcal {G}$ which are ‘uniformly acylindrically hyperbolic’. Our main results reduce this study to sets of homomorphisms which do not diverge in an appropriate sense. As an application, we prove that any relatively hyperbolic group with equationally noetherian peripheral subgroups is itself equationally noetherian.
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Additional Information
  • D. Groves
  • Affiliation: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 S. Morgan Street, Chicago, Illinois 60607
  • MR Author ID: 642547
  • Email:
  • M. Hull
  • Affiliation: Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611
  • MR Author ID: 928123
  • Email:
  • Received by editor(s): March 7, 2018
  • Received by editor(s) in revised form: November 28, 2018
  • Published electronically: May 23, 2019
  • Additional Notes: The first author was partially supported by a grant from the Simons Foundation (#342049) and by NSF grant DMS-1507076.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 7141-7190
  • MSC (2010): Primary 20F65; Secondary 20F67
  • DOI:
  • MathSciNet review: 4024550