2 research outputs found
On the generalized membership problem in relatively hyperbolic groups
The aim of this short note is to provide a proof of the decidability of the
generalized membership problem for relatively quasi-convex subgroups of
finitely presented relatively hyperbolic groups, under some reasonably mild
conditions on the peripheral structure of these groups. These hypotheses are
satisfied, in particular, by toral relatively hyperbolic groups.Comment: 9 pages. An introduction and background section were adde
Algorithms detecting stability and Morseness for finitely generated groups
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 , Kapovich provided a partial algorithm which,
on input a finite set of , halts if generates a quasiconvex subgroup
of 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)