2026-04-14T08:15:56Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/4450882026-02-07T03:11:28Zcom_2072_1033col_2072_452950

Quotient-saturated groups Delgado Rodríguez, Jordi Roy, Mallika Ventura Capell, Enric Universitat Politècnica de Catalunya. Departament de Matemàtiques Universitat Politècnica de Catalunya. GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups Quotient-saturation Congruence extension property Hyperbolic group Acylindrically hyperbolic group 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. 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). Peer Reviewed Postprint (published version) 2025-09 Article Delgado, J.; Roy, M.; Ventura, E. Quotient-saturated groups. «Journal of pure and applied algebra», Setembre 2025, vol. 229, núm. 9, article 108053. 0022-4049 https://arxiv.org/abs/2404.03104 https://hdl.handle.net/2117/445088 10.1016/j.jpaa.2025.108053 eng https://www.sciencedirect.com/science/article/pii/S0022404925001926 http://creativecommons.org/licenses/by/4.0/ Open Access Attribution 4.0 International application/pdf