Related papers: Generalization of order separability for free grou…
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies the properties of the maximal sets of approximate controllability.
We define a notion of free product for coarse spaces that generalizes the corresponding notion of a free product for groups. We show that free products preserve coarse properties such as coarse property C, finite coarse decomposition…
Factors $\frac{X}{Y}$ in a free group $F$ with $Y$ normal in $X$ are considered. Precise results on the free structure of ${Y}$ relative to the free structure of ${X}$ when $\frac{X}{Y}$ is abelian are obtained. Some extensions and…
It is shown that every accessible group which is integrable orbit equivalent to a free group is virtually free. Moreover, we also show that any integrable orbit-equivalence between finitely generated groups extends to their end…
The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…
We show that separability and second-countability are first-order properties among topological spaces definable in o-minimal expansions of $(\mathbb{R},<)$. We do so by introducing first-order characterizations -- definable separability and…
Let M be a B-probability space. Assume that B itself is a D-probability space; then M can be viewed as a D-probability space as well. Let X be in M. We characterize freeness of X from B with amalgamation over D in terms of a certain…
This is a book on Group.
We extend the relation between random matrices and free probability theory from the level of expectations to the level of all correlation functions (which are classical cumulants of traces of products of the matrices). We introduce the…
This is the second part of a series of three articles which introduce laminations for free groups (see math.GR/0609416 for the first part). Several definition of the dual lamination of a very small action of a free group on an $\R$-tree are…
We study algebraic and topological properties of subsets of preorders on a group. In particular we study properties of the composition of two preorders, generalize a topological theorem of \cite{S} in the case of standard orders and show…
This is a review of the results related to generalizations of the notion of $\tau$-function and integrable hierarchies and to their interpretation within the group theory framework that admits an immediate quantization procedure. Different…
The notion of random self-decomposability is generalized further. The notion is then extended to non-negative integer-valued distributions.
A group G is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of G remain non-conjugate in some finite quotient of G. We prove that the free groups and the fundamental…
One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in…
We study the freeness of the group $\mathrm{Inv}(D)$ of invertible ideals of an integral domain $D$, and the freeness of some related groups of (fractional) ideals. We study the relation between $\mathrm{Inv}(D)$ and $\mathrm{Inv}(D_P)$, in…
Some characteristics of the Sawada-Kotera Lagrangian system lend themselves to generalization, producing a large class of separable Lagrangian systems with two degrees of freedom.
We study the properties of the set where a generalized function of bounded variation has infinite approximate limit, highlighting in this way the main geometric difference with functions of bounded variation. To this aim we prove a new…
We develop a theory for describing composite objects in physics. These can be static objects, such as tables, or things that happen in spacetime (such as a region of spacetime with fields on it regarded as being composed of smaller such…
We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on sets of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order…