Related papers: The membership problem for 3-manifold groups is so…
We prove that fundamental groups of orientable (geometrizable) 3-manifolds have a solvable conjugacy problem.
We have proved in [Topology, 45 1 (2006)] that fundamental groups of oriented geometrizable 3-manifolds have a solvable conjugacy problem. We now consider the case of groups of non-oriented geometrizable 3-manifolds in order to conclude…
We study both the Submonoid Membership problem and the Rational Subset Membership problem in finitely generated nilpotent groups. We give two reductions with important applications. First, Submonoid Membership in any nilpotent group can be…
We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the…
We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.
We consider the Membership and the Half-Space Reachability problems for matrices in dimensions two and three. Our first main result is that the Membership Problem is decidable for finitely generated sub-semigroups of the Heisenberg group…
We prove that fundamental groups of non-orientable 3-manifolds have a solvable conjugacy problem, and construct an algorithm. Together with our earlier work on the conjugacy problem in groups on orientable geometrizable 3-manifolds, all…
We show that the word problem for any 3-manifold group is solvable in time $O(n\log^3 n)$. Our main contribution is the proof that the word problem for admissible graphs of groups, in the sense of Croke and Kleiner, is solvable in $O(n\log…
We show that every countable group H with solvable word problem (=computable group) can be subnormally embedded into a 2-generated group G which also has solvable word problem. Moreover, the membership problem for H < G is also solvable. We…
In this paper we show that the membership problems for finitely generated submonoids and for rational subsets are recursively equivalent for groups with two or more ends.
We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type $\mathrm{FP}_\infty$ are virtual retracts. We describe a uniform solution to the membership problem for finitely…
We give a description of finitely generated prosoluble subgroups of the profinite completion of $3$-manifold groups and virtually compact special groups.
In this paper, we compute the subgroup distortion of all finitely generated subgroups of all finitely generated 3-manifold groups, and the subgroup distortion in this case can only be linear, quadratic, exponential and double exponential.…
We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the non-existence of certain forbidden induced subgraphs of the defining…
In this note we prove that every finite collection of connected algebraic subgroups of the group of triangular automorphisms of the affine space generates a connected solvable algebraic subgroup.
The submonoid membership problem for a finitely generated group $G$ is the decision problem, where for a given finitely generated submonoid $M$ of $G$ and a group element $g$ it is asked whether $g \in M$. In this paper, we prove that for a…
We prove that every finitely generated residually finite group $G$ can be embedded in a finitely generated branch group $\Gamma$ such that two elements in $G$ are conjugate in $G$ if and only if they are conjugate in $\Gamma$. As an…
We show that the membership problem in a finitely generated submonoid of a graph group (also called a right-angled Artin group or a free partially commutative group) is decidable if and only if the independence graph (commutation graph) is…
We prove the pro-supersolvable closure of a finitely generated subgroup of the free group is finitely generated. It extends similar results for pro-$p$ closures proved by Ribes-Zalesskii and pro-Nilpotent closures proved by…
In this paper we investigate the decidability and complexity of problems related to braid composition. While all known problems for a class of braids with three strands, $B_3$, have polynomial time solutions we prove that a very natural…