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arXiv · 2404.03104

Quotient-saturated groups

Jordi Delgado·Mallika Roy·Enric Ventura
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Abstract

We introduce the new notion of quotient-saturation as a measure of the immensity of the quotient structure of a group. We present a sufficient condition for a finitely presented group to be quotient-saturated, and use it to 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 this property to finitely presented acylindrically hyperbolic groups.

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Jordi Delgado, Mallika Roy, Enric Ventura. 2024-04-03. Quotient-saturated groups. https://arxiv.org/abs/2404.03104

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