Related papers: Algebraic properties of G-groupoids

The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…

The purpose of this paper is to study the transitive group-groupoids.

The main purpose of this paper is to study the vector groupoids. This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible.

In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.

This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.

The aim of this paper is to describe the definitions and main properties of three generalizations of the group concept, namely: groupoid, generalized group and almost groupoid. Some constructions of these algebraic structures and…

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…

The aim of this paper is to explain, mostly through examples, what groupoids are and how they describe symmetry. We will begin with elementary examples, with discrete symmetry, and end with examples in the differentiable setting which…

The purpose of this paper is to present a systematic exposition of the main results obtained in the studies carried out in groupoid theory. Key words and phrases: groupoid, topological groupoid, Lie groupoid, group-groupoid, vector…

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…

We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the…

This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

Topos properties of the category of covering groupoids over a fixed groupoid are discussed. A classification result for connected covering groupoids over a fixed groupoid analogous to the fundamental theorem of Galois theory is given.

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

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…

Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…

We discuss the basic properties of Lie groupoids, Lie algebroids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and, subsequently, to the integration of partial differential…

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…