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Transactions of the American Mathematical Society

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


Authors: D. Groves and M. Hull
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 20F65; Secondary 20F67
DOI: https://doi.org/10.1090/tran/7789
Published electronically: May 23, 2019
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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
Email: groves@math.uic.edu

M. Hull
Affiliation: Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611
Email: mbhull@ufl.edu

DOI: https://doi.org/10.1090/tran/7789
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