Related papers: Golod-Shafarevich groups: a survey
This thesis studies arithmetic of linear algebraic groups. It involves studying the properties of linear algebraic groups defined over global fields, local fields and finite fields, or more generally the study of the linear algebraic groups…
The purpose of this paper is to study the transitive group-groupoids.
In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.
Inspired by the results of [R. Adin, A. Postnikov, Y. Roichman, Combinatorial Gelfand model, preprint math.RT arXiv:0709.3962], we propose combinatorial Gelfand models for semigroup algebras of some finite semigroups, which include the…
This paper attempts to provide a more or less self-contained introduction into theory of the Grothendieck-Teichmueller group and Drinfeld associators using the theory of operads and graph complexes.
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
This text consists of the introduction, table of contents, and bibliography of a long manuscript (703 pages) that is currently submitted for publication. This manuscript develops an extension of Garside's approach to braid groups and…
Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…
This short paper focuses on Schr\"oder's contribute towards a structural view of group theory.
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
This is a survey paper on the theory of scattered spaces in Galois geometry and its applications.
One important class of tools in the study of the connections between algebraic and topological structures are the "Banach-Stone type theorems", which describe algebraic isomorphisms of algebras (or groups, lattices, etc.) of functions in…
We calculate the Tate-Shafarevich group of an elliptic three-fold $f:X\rightarrow S$ when $X$ and $S$ are regular and $f$ is flat, relating it to the Brauer group of $X$ and $S$. We show that given certain hypotheses on $f$, the…
For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…
This paper classifies the derivations of twisted group algebras in terms of the generators and defining relations of the group. In particular, we generalize some know results over group algebras to the case of twisted group algebras. We…
Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that…
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how…
A short survey on applications of algebraic geometry in topological data analysis.
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…