Ascending Chains of Free Quasiconvex Subgroups
Jack Kohav, Nir Lazarovich
TL;DR
This paper proves that in hyperbolic groups, there are no infinite strictly ascending chains of free quasiconvex subgroups with fixed rank, revealing structural limitations of subgroup arrangements.
Contribution
It establishes a new restriction on subgroup chains in hyperbolic groups, specifically ruling out infinite ascending sequences of free quasiconvex subgroups of constant rank.
Findings
No strictly ascending chains of free quasiconvex subgroups of fixed rank exist in hyperbolic groups.
Provides structural insights into subgroup configurations within hyperbolic groups.
Enhances understanding of subgroup hierarchy constraints in geometric group theory.
Abstract
We prove that a hyperbolic group cannot contain a strictly ascending chain of free quasiconvex subgroups of constant rank.
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Taxonomy
TopicsRings, Modules, and Algebras · Fuzzy and Soft Set Theory · Advanced Topology and Set Theory