Related papers: Approximate (Abelian) groups
We are generalizing in two non-trivial ways the recently defined perspective Abelian groups to the so-called IC-groups and TP-groups, respectively, and obtain numerous results in these two directions that can be viewed as improvements on…
In this notebook, I present duality theory (or theories) of abelian groups with some categorical and categorical topological flavour. I consider writing this notebook as a longer-term project, and its current content and presentation is…
We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…
We comment on the paper "Extremal Cayley digraphs of finite Abelian groups" [Intercon. Networks 12 (2011), no. 1-2, 125--135]. In particular, we give some counterexamples to the results presented there, and provide a correct result for…
We report new examples of Sidon sets in abelian groups arising from generalized jacobians of curves, and discuss some of their properties with respect to size and structure.
It is proved that, for a wide class of topological abelian groups (locally quasi--convex groups for which the canonical evaluation from the group into its Pontryagin bidual group is onto) the arc component of the group is exactly the union…
We classify smooth projective surfaces that are quotients of abelian surfaces by finite groups.
We prove an arithmetic regularity lemma for stable subsets of finite abelian groups, generalising our previous result for high-dimensional vector spaces over finite fields of prime order. A qualitative version of this generalisation was…
This survey paper aims at giving the state of the art in the study of string C-group representations of almost simple groups. It also suggest a series of problems and conjectures to the interested reader.
For some countable discrete torsion Abelian groups we give examples of their finite measure-preserving actions which have simple spectrum and no approximate transitivity property.
This article continues a prior investigation of the authors with the goal of extending characterization results of convolutional tight frames from the context of cyclic groups to general finite abelian groups. The collections studied are…
In this short note we give a formula for the number of chains of subgroups of a finite elementary abelian $p$-group. This completes our previous work [5].
The group of almost Riordan arrays contains the group of Riordan arrays as a subgroup. In this note, we exhibit examples of pseudo-involutions, involutions and quasi-involutions in the group of almost Riordan arrays.
We study topological groups that can be defined as Polish, pro-countable abelian groups, as non-archimedean abelian groups or as quasi-countable abelian groups, i.e., Polish subdirect products of countable, discrete groups, endowed with the…
In this paper, we investigate the structure of associated groups of symmetric quandles. Among other results, we explore the relationship between the associated group of a symmetric quandle and that of its underlying quandle. We provide a…
In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we…
We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.
The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…
We give lower bounds for dimensions of the centers of Hodge groups of superelliptic jacobians. In "generic case" this bound is precise. We also discuss dimensions of simple abelian subvarieties of superelliptic jacobians.
A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group $G$. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over…