相关论文: Measure free factors of free groups
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand,…
We give a positive answer, in the measurable-group-theory context, to von Neumann's problem of knowing whether a non-amenable countable discrete group contains a non-cyclic free subgroup. We also get an embedding result of the free-group…
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…
In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.
We establish new characterizations of primitive elements and free factors in free groups, which are based on the distributions they induce on finite groups. For every finite group $G$, a word $w$ in the free group on $k$ generators induces…
An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…
A classification of the ways in which an element of a free group can be expressed as a product of commutators or as a product of squares is given. This is then applied to some particular classes of elements. Finally, a question about…
We are now witnessing a rapid growth of a new part of group theory which has become known as "statistical group theory". A typical result in this area would say something like ``a random element (or a tuple of elements) of a group G has a…
In this note we give a new proof of the fact that an elementary subgroup (in the sense of first-order theory) of a non abelian free group $\mathbb{F}$ must be a free factor. The proof is based on definability of orbits of elements of under…
The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and…
We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lueck-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In…
It was proved that for any finite set of elements of a free product of residually finite groups such that no two of them belong to conjugate cyclic subgroups and each of them do not belong to a subgroup which is conjugate a to free factor…
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index…
Can one detect free products of groups via their profinite completions? We answer positively among virtually free groups. More precisely, we prove that a subgroup of a finitely generated virtually free group $G$ is a free factor if and only…
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often…
We introduce the definition of totally nonfree actions of groups; such actions are naturally related to the theory of characters of groups and their factor-representations of type II. This short note is a brief exposition of a part of a…
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…
Since the 1970's, physicists and mathematicians who study random matrices in the GUE or GOE models are aware of intriguing connections between integrals of such random matrices and enumeration of graphs on surfaces. We establish a new…