dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
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Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics
dc.contributor.author
Delgado Rodríguez, Jordi
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Roy, Mallika
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Ventura Capell, Enric
dc.identifier
Delgado, J.; Roy, M.; Ventura, E. Quotient-saturated groups. «Journal of pure and applied algebra», Setembre 2025, vol. 229, núm. 9, article 108053.
dc.identifier
https://arxiv.org/abs/2404.03104
dc.identifier
https://hdl.handle.net/2117/445088
dc.identifier
10.1016/j.jpaa.2025.108053
dc.description.abstract
We introduce the new notion of quotient-saturation as a measure of the immensity of the quotient structure of a group, and we prove that it is a necessary condition for a non-elementary finitely presented group to embed in a hyperbolic group. More generally, we present a sufficient condition — called Congruence Extension Property equipment (in short, CEP-equipment) — for a finitely presented group to be quotient-saturated. Using this property, we deduce that non-elementary finitely presented subgroups of a hyperbolic group (in particular, non-elementary hyperbolic groups themselves) are quotient-saturated. Finally, we elaborate on the previous results to extend the scope of CEP-equipment (and hence of quotient-saturation) to finitely presented acylindrically hyperbolic groups.
dc.description.abstract
The first named author thanks the support from the Universitat Politècnica de Catalunya (UPC) through a María Zambrano grant. The second named author thanks the support from UPC through a Margarita Salas grant. The three authors acknowledge support from the Spanish Agencia Estatal de Investigación through grant PID2021-126851NB-100 (AEI/ FEDER, UE).
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Peer Reviewed
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Postprint (published version)
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application/pdf
dc.relation
https://www.sciencedirect.com/science/article/pii/S0022404925001926
dc.rights
http://creativecommons.org/licenses/by/4.0/
dc.rights
Attribution 4.0 International
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups
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Quotient-saturation
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Congruence extension property
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Hyperbolic group
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Acylindrically hyperbolic group
dc.title
Quotient-saturated groups
