Related papers: On an algorithm to decide whether a free group is …
Let G be a word-hyperbolic group with given finite generating set, for which various standard structures and constants have been pre-computed. A (non-practical) algorithm is described that, given as input two lists A and B, each composed of…
We consider the set of finite random words $\mathcal A^\star$, with independent letters drawn from a finite or infinite totally ordered alphabet according to a general probability distribution. On a specific subset of $\mathcal A^\star$,…
We begin the investigation of the free factor complex of a free group of finite rank. For the case of rank 2 we axiomatize its theory and show that it is $\omega$-stable with prime model $AF_2$.
In this paper we develop techniques that eliminate the need of the Generalized Riemann Hypothesis (GRH) from various (almost all) known results about deterministic polynomial factoring over finite fields. Our main result shows that given a…
Let G be any locally compact, unimodular, metrizable group. The main result of this paper, roughly stated, is that if F<G is any finitely generated free group and \Gamma < G any lattice, then up to a small perturbation and passing to a…
The mapping torus induced by an automorphism $\phi$ of the free abelian group $\mathbb{Z}^n$ is a semi-direct product $G=\mathbb{Z}^n\rtimes_\phi \mathbb{Z}$. We show that whether the rank of $G$ is equal to $n+1$ is decidable. As a…
We prove that for a finitely generated group G with a free factor system and an injective endomorphism that preserves the free factor system, the ascending HNN extension of G is hyperbolic relative to a collection of maximal parabolic…
We present an algorithm for the following problem: given a context-free grammar for the word problem of a virtually free group $G$, compute a finite graph of groups $\mathcal{G}$ with finite vertex groups and fundamental group $G$. Our…
We propose an algorithm which for any recursive group $G$, given by its effectively enumerable generators and recursively enumerable relations, outputs an explicit embedding of $G$ into a finitely presented group directly written by its…
If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is flexible enough to find factors subject to additional…
We show that for a fixed free group F and an arbitrary finitely generated subgroup H (as given above) we can perform the Stalling's folding process in time O(N log^*(N)), where N is the sum of the word lengths of the given generators of H.
The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated free group factor $L(\freeF_r)$. The finite…
We address the noncommutative version of the Edmonds' problem, which asks to determine the inner rank of a matrix in noncommuting variables. We provide an algorithm for the calculation of this inner rank by relating the problem with the…
Let $F$ be either a free nilpotent group of a given class and of finite rank or a free solvable group of a certain derived length and of finite rank. We show precisely which ones have the $R_{\infty}$ property. Finally, we also show that…
It was proved by Sela and by the authors that every formula in the theory of a free group $F$ is equivalent to a boolean combination of $\exists\forall$-formulas. We also proved that the elementary theory of a free group is decidable (there…
Let $G$ be a finite solvable group, given through a refined consistent polycyclic presentation, and $\alpha$ an automorphism of $G$, given through its images of the generators of $G$. In this paper, we discuss algorithms for computing the…
We prove that a semigroup generated by a reversible two-state Mealy automaton is either finite or free of rank 2. This fact leads to the decidability of finiteness for groups generated by two-state or two-letter invertible-reversible Mealy…
We prove that if F is a finitely generated free group and f:F -> F is an automorphism with polynomial growth of degree d, then there exists a characteristic subgroup S < F of finite index such that the induced automorphism of the…
We derive a lower and an upper bound for the rank of the finite part of operator $K$-theory groups of maximal and reduced $C^*$-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing conjugacy…
Voiculescu's random matrix model for freeness is extended to the non-Gaussian case and also the case of constant block diagonal matrices. Thus we are able to investigate free products of free group factors with matrix algebras and with the…