Related papers: Parabolic subgroups and word problem in virtual Ar…

There exist right angled Artin groups $A$ such that the isomorphism problem for finitely presented subgroups of $A$ is unsolvable, and for certain finitely presented subgroups the conjugacy and membership problems are unsolvable. It follows…

We conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial factors ss^{-1} or s^{-1}s. Here we make this statement precise and explain how it can be seen as a weak form of hyperbolicity. We prove the…

This article studies the complexity of the word problem in groups of automorphisms of subshifts. We show in particular that for any Turing degree, there exists a subshift whose automorphism group contains a subgroup whose word problem has…

We classify the Artin groups that admit retractions onto all of their parabolic subgroups. Our approach relies on a detailed analysis of triangular subgroups, with a key ingredient being the classification of homomorphisms between dihedral…

$2$-stratifolds are a generalization of $2$-manifolds in that there are disjoint simple closed curves where several sheets meet. We show that the word problem for fundamental groups of $2$-stratifolds is solvable.

We show a simple and easily implementable solution to the word problem for virtual braid groups.

We give a simple algorithm to solve the subgroup membership problem for virtually free groups. For a fixed virtually free group with a fixed generating set $X$, the subgroup membership problem is uniformly solvable in time $O(n\log^*(n))$…

We study groups of reversible cellular automata, or CA groups, on groups. More generally, we consider automorphism groups of subshifts of finite type on groups. It is known that word problems of CA groups on virtually nilpotent groups are…

We investigate the average-case complexity of decision problems for finitely generated groups, in particular the word and membership problems. Using our recent results on ``generic-case complexity'' we show that if a finitely generated…

Let $A_\Gamma$ be an Artin group with defining graph $\Gamma$. We introduce the notion of $A_\Gamma$ being extra-large relative to a family of arbitrary parabolic subgroups. This generalizes a related notion of $A_\Gamma$ being extra-large…

We give a short proof for the fact, already proven by Thomas Haettel, that the arbitrary intersection of parabolic subgroups in Euclidean Braid groups $A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the…

We study the outer automorphism group of a right-angled Artin group $A_\Gamma$ with finite defining graph $\Gamma$. We construct a subnormal series for $Out(A_\Gamma)$ such that each consecutive quotient is either finite, free-abelian,…

It is shown that for graph groups (right-angled Artin groups) the conjugacy problem as well as a restricted version of the simultaneous conjugacy problem can be solved in polynomial time even if input words are represented in a compressed…

We explore a natural class of semigroups that have word problem decidable by finite state automata. Among the main results are invariance of this property under change of generators, invariance under basic algebraic constructions and…

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…

We show that the Word Problem in finitely generated subgroups of $\textsf{GL}_d(\mathbb{Z})$ can be solved in linear average-case complexity. This is done under the bit-complexity model, which accounts for the fact that large integers are…

*by a standard (one-tape) Turing machine. It is well-known that the word problem for hyperbolic groups, whence in particular for free groups, can be solved in linear time. However, these algorithms run on machines more complicated than a…

We prove that an arbitrary right-angled Artin group $G$ admits a quasi-isometric group embedding into a right-angled Artin group defined by the opposite graph of a tree. Consequently, $G$ admits quasi-isometric group embeddings into a pure…

In this paper we solve the conjugacy problem for several classes of virtual right-angled Artin groups, using algebraic and geometric techniques. We show that virtual RAAGs of the form $A_{\phi} = A_{\Gamma} \rtimes_{\phi}…

A special inverse monoid is one defined by a presentation where all the defining relations have the form $r = 1$. By a result of Ivanov Margolis and Meakin the word problem for such an inverse monoid can often be reduced to the word problem…