Related papers: Quadratic equations in the Grigorchuk group

The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…

We prove that if a group possesses a deficiency 1 presentation where one of the relators is a commutator then it is the integers times the integers, is large, or is as far as possible from being residually finite. Then we use this to show…

We find an upper bound for the Gromov width of coadjoint orbits of compact Lie groups with respect to the Kirillov Kostant Souriau form by computing certain Gromov Witten invariants, the approach presented here is closely related to the one…

We present an algorithm which decides whether a given quasiconvex residually finite subgroup $H$ of a hyperbolic group $G$ is associated with a splitting. The methods developed also provide algorithms for computing the number of filtered…

The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…

Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We…

We investigate the complexity of computing the Zariski closure of a finitely generated group of matrices. The Zariski closure was previously shown to be computable by Derksen, Jeandel, and Koiran, but the termination argument for their…

The reality of the difficulties in investigation of finite groups are considered. It is shown that the consideration of symmetry properties of the $k$-orbits that are obtained with an action of a finite group $F=(V,\cdot)$ on Cartesian…

Using the circle method, we obtain asymptotic formulae for the number of integer solutions to certain quadratic polynomials that are uniform in the coefficients of the polynomial.

We present an algorithm that determines the Galois group of linear difference equations with rational function coefficients.

We present an algorithm that decides whether a finitely generated linear group over an infinite field is solvable-by-finite: a computationally effective version of the Tits alternative. We also give algorithms to decide whether the group is…

In 1977, Makanin established the decidability of equations in free monoids. A key ingredient in his proof is the exponent of periodicity: for a word $w$, it is the largest exponent $e$ such that $w$ contains a nonempty factor of the form…

This paper investigate bounds of the commutator width \cite {Mur} of a wreath product of two groups. The commutator width of direct limit of wreath product of cyclic groups are found. For given a permutational wreath product sequence of…

We find a new class of the Fuchsian equations, which have an algebraic geometric solutions with the parameter belonging to a hyperelliptic curve. Methods of calculating the algebraic genus of the curve, and its branching points, are…

Solutions of a linear equation b=ax in a homomorphic image of a commutative Bezout domain of stable range 1.5 is developed. It is proved that the set of solutions of a solvable linear equation contains at least one solution that divides the…

We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…

We prove combination theorems in the spirit of Klein and Maskit in the context of discrete convergence groups acting geometrically finitely on their limit sets. As special cases, we obtain combination theorems for geometrically finite…

Let $G$ be a finite group. We show that the order of the subgroup generated by coprime $\gamma_k$-commutators (respectively $\delta_k$-commutators) is bounded in terms of the size of the set of coprime $\gamma_k$-commutators (respectively…

Let $G$ be a profinite group. We prove that the commutator subgroup $G'$ is finite-by-procyclic if and only if the set of all commutators of $G$ is contained in a union of countably many procyclic subgroups.

We present and solve a Linear Quadratic Regulator (LQR) for the boundary control of the beam equation. We use the simple technique of completing the square to get an explicit solution. By decoupling the spatial frequencies we are able to…