Related papers: Equations in a free group. Elementary theory
It is shown how to map the quantum states of a system of free Bose particles one-to-one onto the states of a completely deterministic model. It is a classical field theory with a large (global) gauge group.
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
In this work the author studies the property close to property of order separability.
We prove that no infinite field is interpretable in the first-order theory of nonabelian free groups. We also obtain a characterization of Abelian groups interpretable in this theory.
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
Our main goal is to study the freeness of Sch\"utzenberger groups defined by primitive substitutions. Our findings include a simple freeness test for these groups, which is applied to exhibit a primitive invertible substitution with…
Free products of two residually finite groups with amalgamated retracts are considered. It is proved that a cyclic subgroup of such a group is not finitely separable if, and only if, it is conjugated with a subgroup of a free factor which…
The existence of an infinite simple boundedly generated 2-generated group and the existence of a boundedly simple 2-generated group containing a free non-cyclic subgroup are proved.
Our purpose is to visualize the pronilpotent completion of a finitely generated free group as a certain subgroup in the free Lie group.
Recently Ould Houcine-Tent (see arXiv:1205.0929v2 [math.GR]) proved that the theory of non abelian free groups is $n$-ample for any $n<\omega$. We give a sequence of single elements in $F_{\omega}$ witnessing the above mentioned result. Our…
We prove a mean ergodic theorem for amenable discrete quantum groups. As an application, we prove a Wiener type theorem for continuous measures on compact metrizable groups.
For a group acting on a hyperbolic space, we set up an algorithm in the group algebra showing that ideals generated by few elements are free, where few is a function of the minimal displacement of the action, and derive algebraic,…
In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.
We give a new criterion for solvability of group equations, providing proofs of various generalizations of the Kervaire-Laudenbach conjecture for Connes-embeddable groups.
We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in…
Every endofunctor of the category of classes is proved to be set-based in the sense of Aczel and Mendler, therefore, it has a final coalgebra. Other basic properties of these endofunctors are proved, e.g. the existence of a free completely…
We show that every distributive lattice-ordered pregroup can be embedded into a functional algebra over an integral chain, thus improving the existing Cayley/Holland-style embedding theorem. We use this to show that the variety of all…
In this work we investigate tensor completions of groups by associative rings, which were introduced by R.Lyndon and G.Baumslag in 1960s. The main result states that there exists an algorithm that decides if a given finite system of…
We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in…
We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coincides with the positive theory of a non-abelian free group.…