Algorithms detecting stability and Morseness for finitely generated groups

DOI10.1016/J.JALGEBRA.2020.03.002arXiv1908.04460MaRDI QIDQ6323576

Heejoung Kim

Publication date: 12 August 2019

Abstract: The notions of stable and Morse subgroups of finitely generated groups generalize the concept of a quasiconvex subgroup of a word-hyperbolic group. For a word-hyperbolic group $G$, Kapovich provided a partial algorithm which, on input a finite set $S$ of $G$, halts if $S$ generates a quasiconvex subgroup of $G$ and runs forever otherwise. In this paper, we give various detection and decidability algorithms for stability and Morseness of a finitely generated subgroup of mapping class groups, right-angled Artin groups, toral relatively hyperbolic groups, and finitely generated groups discriminated by a locally quasiconvex torsion-free hyperbolic group (for example, ordinary limit groups).

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Geometric group theory (20F65) Topological methods in group theory (57M07) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Hyperbolic groups and nonpositively curved groups (20F67)

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