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Transactions of the American Mathematical Society

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



Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families

Authors: D. Groves and M. Hull
Journal: Trans. Amer. Math. Soc. 372 (2019), 7141-7190
MSC (2010): Primary 20F65; Secondary 20F67
Published electronically: May 23, 2019
MathSciNet review: 4024550
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Abstract: 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

M. Hull
Affiliation: Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611
MR Author ID: 928123

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.
Article copyright: © Copyright 2019 American Mathematical Society