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It is proven that if a finitely presented group is one ended it has asymptotic dimension bigger than one. It follows that finitely presented groups with asdim 1 are virtually free. A counterexample is given for the finitely generated case.
Dimensions like Gelfand, Krull, Goldie have an intrinsic role in the study of theory of rings and modules. They provide useful technical tools for studying their structure. In this paper we define one of the dimensions called couniserial…
The first part of the paper centers in the study of embeddability between partially commutative groups. In [KK], for a finite simplicial graph $\Gamma$, the authors introduce an infinite, locally infinite graph $\Gamma^e$, called the…
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroups with embedding dimension three.
This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been…
We introduce the notion of noncommutative complex spheres with partial commutation relations for the coordinates. We compute the corresponding quantum symmetry groups of these spheres, and this yields new quantum unitary groups with partial…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…
This is the third paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. We give generalizations of the well known fact that a nontrivial commutator in a free group is not a proper power to both graphs of…
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…
We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…
Let $X$ be a finite set. Let $\mathcal{T}(X)$ be the transformation semigroup on $X$ and let $\mathcal{P}(X)$ be the partial transformation semigroup on $X$. This paper is a contribution to the problem of characterizing the largest…
This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to…
The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint type, we construct a smooth, log-symplectic fiberwise…
Sufficient dimension reduction methods often require stringent conditions on the joint distribution of the predictor, or, when such conditions are not satisfied, rely on marginal transformation or reweighting to fulfill them approximately.…
The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…
We obtain a characteristic-free decomposition of tensor space, regarded as a module for the Brauer centralizer algebra.
We describe a simple approach to factorize non-commutative (nc) polynomials, that is, elements in free associative algebras (over a commutative field), into atoms (irreducible elements) based on (a special form of) their minimal linear…
We introduce notions of a constraint metric approximation and of a constraint stability of a metric approximation. This is done in the language of group equations with coefficients. We give an example of a group which is not constraintly…
Deep Neural Networks have achieved remarkable success relying on the developing high computation capability of GPUs and large-scale datasets with increasing network depth and width in image recognition, object detection and many other…