Related papers: The theorems on freedom for relatively free groups…

In this paper we prove that the Morse boundary of a free product depends only on the Morse boundary of its factors. In fact, we also prove the analogous result for graphs of groups with finite edge groups and infinitely many ends. This is a…

In \cite{BAMU}, an ergodic theorem \`a la Birkhoff-von Neumann for the action of the fundamental group of a compact negatively curved manifold on the boundary of its universal cover is proved. A quick corollary is the irreducibility of the…

A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.

We prove a generalization of the classical Klein-Maskit combination theorem, in the free product case, in the setting of Anosov subgroups. Namely, if $\Gamma_A$ and $\Gamma_B$ are Anosov subgroups of a semisimple Lie group $G$ of noncompact…

The Friedman--Mineyev theorem, earlier known as the (strengthened) Hanna Neumann conjecture, gives a sharp estimate for the rank of the intersection of two subgroups in a free group. We obtain an analogue of this inequality for any two…

We prove a ratio ergodic theorem for amenable equivalence relations satisfying a strong form of the Besicovich covering property. We then use this result to study general non-singular actions of non-abelian free groups and establish a ratio…

In [FGRS1,FGRS2] the relationship between the universal and elementary theory of a group ring $R[G]$ and the corresponding universal and elementary theory of the associated group $G$ and ring $R$ was examined. Here we assume that $R$ is a…

Relations and interactions between the theorems of Ash, Herwig--Lascar and Ribes--Zalesskii are discussed and it is shown that these three theorems are equivalent in the sense that each of them can be derived from each other one. Some…

We construct easy embeddings of relatively free groups (say the free Burnside group, the free solvable group) into finitely presented groups. We introduce a concept of verbal isoperimetric function of a group variety. We prove that if the…

We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is…

We show that some results of L. Makar-Limanov, P. Malcolmson and Z. Reichstein on the existence of free associative algebras are valid in the more general context of varieties of algebras.

This note provides an alternate account of Calegari's rationality theorem for stable commutator length in free groups.

We propose a new look at the Julg-Valette theorem on K-theoretic amenability for groups operating on trees. The main tool is a generalization of a construction of uniformly bounded representations of the free groups due to Pytlik and…

In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…

Sets of solutions to finite systems of equations in a free group, are equivalent to sets of homomorphisms from a fixed f.p. group into a free group. The latter can be encoded in a diagram, the construction of which is valid also for f.g.…

Two measures of how near an arbitrary function between groups is to being a homomorphism are considered. These have properties similar to conjugates and commutators. The authors show that there is a rich theory based on these structures,…

Free-minor closed classes [2] and free-planar graphs [3] are considered. Versions of Kuratowski-like theorem for free-planar graphs and Kuratowski theorem for planar graphs are considered.

We show that the level sets of automorphisms of free groups with respect to the Lipschitz metric are connected as subsets of Culler-Vogtmann space. In fact we prove our result in a more general setting of deformation spaces. As…