Related papers: On the isolated points in the space of groups

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

A necessary condition for uniqueness of factorizations of elements of a finite group $G$ with factors belonging to a union of some conjugacy classes of $G$ is given. This condition is sufficient if the number of factors belonging to each…

This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…

This paper investigates the finite generation of cluster automorphism groups. By applying the pseudo $\mathbb{N}$-grading introduced in our previous work, we establish a sufficient condition for a cluster automorphism group to be finitely…

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…

We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of…

We consider the group property of being icc. We give several examples of icc groups and study its stability under usual algebraic constructions.

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We describe the endomorphisms of the direct product of two free groups of finite rank and obtain conditions for which the subgroup of fixed points is finitely generated and we do the same for periodic points. We also describe the…

This survey paper presents the discrete group viewpoint on Kac-Moody groups. Over finite fields, the latter groups are finitely generated; they act on new buildings enjoying remarkable negative curvature properties. The study of these…

In this paper we examine various properties/constructions which are known for reductive groups and we do some experiments to see to what extent they generalize to symmetric spaces.

We study finite groups which possess a strongly p-embedded subgroup for some odd prime p. The main results of the paper will be applied in the ongoing project to classify the simple groups of local characteristic p.

Theorems on the existence of vector fields with given sets of Indexes of isolated Singular points are proved for the cases of closed manifolds, pairs of manifolds, manifolds with boundary, and gradient fields. It is proved that, on a…

This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…

PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.

We introduce the concepts of a pair of valuations and a good generating set and show how they can be used to prove geometric properties of soluble groups.

The aim of this note is to give an easy example of a finitely presented group that cannot act without a fix point on a CAT(0) space of finite dimension. Such an example has been recently constructed by Arjantseva et al., using other…

This article explores the interplay between the finite quotients of finitely generated residually finite groups and the concept of amenability. We construct a finitely generated, residually finite, amenable group $A$ and an uncountable…

In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…