Related papers: The conjugacy problem for positive homogeneously p…
Every semigroup which is a finite disjoint union of copies of the free mono- genic semigroup (natural numbers under addition) has soluble word prob- lem and soluble membership problem. Efficient algorithms are given for both problems.
There exist combable groups in which the conjugacy problem is unsolvable. The isomorphism problem is unsolvable for certain recursive sequences of finite presentations of combable groups.
We establish an Ando-type dilation theorem for a pair of commuting contractions together with a representation of a right LCM monoid via either the Cartesian or the free product. We prove that if each individual contraction together with…
Guba and Sapir asked if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give a solution to the latter question using elementary techniques which rely purely on the description of F…
Motivated by its applications to the word problem for one-relator inverse monoids, via results of Ivanov, Margolis, and Meakin (2001), we prove several decidability and undecidability results about the submonoid membership problem in…
We investigate gcd-monoids, which are cancellative monoids in which any two elements admit a left and a right gcd, and the associated reduction of multifractions (arXiv:1606.08991 and 1606.08995), a general approach to the word problem for…
By classical results of Malcev, cancellative monoids need not be group-embeddable. In this paper, we describe and give presentations for and study an infinite family $\mathcal{M}_n$ of cancellative monoids which are not group-embeddable,…
In this paper, a connection between rewriting systems and embedding of monoids in groups is found. We show that if a group with a positive presentation has a complete rewriting system $\Re$ that satisfies the condition that each rule in…
Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or…
We solve the simultaneous conjugacy problem in Artin's braid groups and, more generally, in Garside groups, by means of a complete, effectively computable, finite invariant. This invariant generalizes the one-dimensional notion of super…
In an additive factorial monoid each element can be represented as a linear combination of irreducible elements (atoms) with uniquely determined coefficients running over all natural numbers. In this paper we develop for a wide class of…
The set of all cancellable elements of the lattice of semigroup varieties has recently been shown to be countably infinite. But the description of all cancellable elements of the lattice $\mathbb{MON}$ of monoid varieties remains unknown.…
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…
An effective theory is proposed, combining the standard gauge group $SU(3)_{C}\otimes SU(2)_{L}\otimes U(1)_{Y}$ with a horizontal discrete symmetry. By assigning appropriate charges under this discrete symmetry to the various fermion…
We investigate the generalized moment membership problem for matrices, a formulation equivalent to Skolem's problem for linear recurrence sequences. We show decidability for orthogonal, unitary, and real eigenvalue matrices, and…
We study the conjugacy problem in cyclic extensions of free groups. It is shown that the conjugacy problem is solvable in split extensions of finitely generated free groups by virtually inner automorphisms. An algorithm for construction of…
Let $G$ be a finite group, and let $\kappa(G)$ be the probability that elements $g$, $h\in G$ are conjugate, when $g$ and $h$ are chosen independently and uniformly at random. The paper classifies those groups $G$ such that $\kappa(G) \geq…
We design new deterministic and randomized algorithms for computational problems in free solvable groups. In particular, we prove that the word problem and the power problem can be solved in quasi-linear time and the conjugacy problem can…
We show thatthe double reversing algorithm proposed by dehornoy for solving the word problem in the braid group can also be used to recognize the conjugates of powers of the generators in an Artin group of spherical type. The proof uses a…
Many results have been established that show how arithmetic conditions on conjugacy class sizes affect group structure. A conjugacy class in $G$ is called vanishing if there exists some irreducible character of $G$ which evaluates to zero…