Related papers: Implicit function theorem over free groups

We investigate which free constructions (amalgamated products and HNN-extensions) over word hyperbolic groups produce groups that are again word hyperbolic. A complete answer is obtained for the case when the amalgamated subgroups are…

We formulate some global invertibility and implicit function theorems. We extend the result of Idczak, Skowron and Walczak on the invertibility of the operators to the case of the operators with critical points. The proof relies on the…

Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a…

In this paper, we give an affirmative answer to Yamada's Conjecture on free topological groups, which was posed in [K. Yamada, {\it Fr\'echet-Urysohn spaces in free topological groups}, Proc. Amer. Math. Soc., {\bf 130}(2002), 2461--2469.].

Let $k$ be a field of characteristic different from $2$ and let $G$ be a nonabelian residually torsion-free nilpotent group. It is known that $G$ is an orderable group. Let $k(G)$ denote the subdivision ring of the Malcev-Neumann series…

In this paper, we prove a version of the arithmetic Bertini theorem asserting that there exists a strictly small and generically smooth section of a given arithmetically free graded arithmetic linear series.

We extend the notion of generalized Whittaker models by allowing them to be built upon smooth irreducible representations of unipotent subgroups of a $p$-adic reductive group that are not necessarily characters, nor induced from Weil…

We present a polynomial time exact quantum algorithm for the hidden subgroup problem in $Z_{m^k}^n$. The algorithm uses the quantum Fourier transform modulo m and does not require factorization of m. For smooth m, i.e., when the prime…

We prove various results connecting structural or algebraic properties of graphs and groups to conditions on their spaces of harmonic functions. In particular: we show that a group with a finitely supported symmetric measure has a…

This paper has two parts. We first survey recent efforts on the Bloom conjecture which still remains open in the case of complex dimension at least 4. Bloom's conjecture concerns the equivalence of three regular types. There is a more…

We establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all $n\in\mathbb{N}$, a residually free group is of…

Let $K$ be a number field or a function field. Let $f\in K(x)$ be a rational function of degree $d\geq 2$, and let $\beta\in\mathbb{P}^1(K)$. For all $n\in\mathbb{N}\cup\{\infty\}$, the Galois groups…

In 2006 Z. Sela and independently O. Kharlampovich and A. Myasnikov gave a solution to the Tarski problems by showing that two non-abelian free groups have the same elementary theory. Subsequently Z. Sela generalized the techniques used in…

We present a non-commutative version of the cycle lemma of Dvoretsky and Motzkin that applies to free groups and use this result to solve a number of problems involving cyclic reduction in the free group. We also describe an application to…

The article is devoted to investigation of applications of infinite systems of functional equations for modeling of functions with complicated local structure, that are defined in terms of the nega-$\tilde Q$-representation. The infinite…

The goal of this note is to provide yet another proof of the following theorem of Golod: there exists an infinite finitely generated group $G$ such that every element of $G$ has finite order. Our proof is based on the Nielsen-Schreier index…

We show that for any finitely generated group of matrices that is not virtually solvable, there is an integer m such that, given an arbitrary finite generating set for the group, one may find two elements a and b that are both products of…

We prove that, for a finitely generated group hyperbolic relative to virtually abelian subgroups, the generalised word problem for a parabolic subgroup is the language of a real-time Turing machine. Then, for a hyperbolic group, we show…

We resolve the Grothendieck-Serre question over an arbitrary base field $k$: for a smooth $k$-group scheme $G$ and a smooth $k$-variety $X$, we show that every generically trivial $G$-torsor over $X$ trivializes Zariski semilocally on $X$.…

We prove that the generalised word problem of a finitely generated subgroup of a finitely generated virtually free group is context-free, that a hyperbolic group must be virtually free if it has a torsion-free quasiconvex subgroup of…