Related papers: Normal Soft int-Group
The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…
For an arbitrary connected solvable spherical subgroup H of a connected semisimple algebraic group G we compute the group N_G(H), the normalizer of H in G. Thereby we complete a classification of all (not necessarily connected) solvable…
We present a natural extension of the process of taking a group quotient to arbitrary subgroups. We first review basic concepts from group theory. This will allow us to see the relationship between our new, more general quotient operation…
Soft set theory and rough set theory are mathematical tools to deal with uncertainties. In [3], authors combined these concepts and introduced soft rough sets. In this paper, we introduce the concepts of soft rough graphs, vertex and edge…
In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…
Let $X$ be a finite set such that $|X|=n$. Let $\trans$ and $\sym$ denote respectively the transformation monoid and the symmetric group on $n$ points. Given $a\in \trans\setminus \sym$, we say that a group $G\leq \sym$ is $a$-normalizing…
In this study, the soft usual topology compatible with the usual topology of $\mathbb{R}$ is defined, and using its subspace topology on the interval $[0,1]$, the concept of a soft path is introduced. Within this context, the notions of…
For a group $G$, a {\it normalizer covering} of $G$ is a finite set of proper normalizers of some subgroups of $G$ whose union is $G$. We study $p$-groups ($p$ a prime) without a normalizer covering. As an application, we determine some…
We study the class of groups having the property that every non-nilpotent subgroup is equal to its normalizer. These groups are either soluble or perfect. We completely describe the structure of soluble groups and finite perfect groups with…
In this paper, the definitions of soft {\Gamma}-semirings and soft sub {\Gamma}-semi rings are introduced with the aid of the concept of soft set theory introduced by Molodtsov. In the mean time, some of their properties and structural…
We introduce a class of automorphisms of compact quantum groups which may be thought of as inner automorphisms and explore the behaviour of normal subgroups of compact quantum groups under these automorphisms. We also define the notion of…
In this paper we introduce and study the concept of normality degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be normal. Explicit formulas are obtained for some particular classes of…
First of all, we focused soft {\beta}-open sets and soft {\beta}-closed sets over the soft topological space and investigated some properties of them. Secondly, we defined the concepts soft {\beta}-continuity, soft {\beta}-irresolute and…
In this paper, we give an introduction for rough groups and rough homomorphisms. Then we present some properties related to topological rough subgroups and rough subsets. We construct the product of topological rough groups and give an…
We first compare several algebraic notions of normality, from a categorical viewpoint. Then we introduce an intrinsic description of Higgins' commutator for ideal-determined categories, and we define a new notion of normality in terms of…
A group $G$ is said to have dense normalizers if each non-empty open interval in its subgroup lattice $L(G)$ contains the normalizer of a certain subgroup of $G$. In this note, we find all finite groups satisfying this property. We also…
In this book, the authors define several new types of soft neutrosophic algebraic structures over neutrosophic algebraic structures and we study their generalizations. These soft neutrosophic algebraic structures are basically parameterized…
We investigate the notion of a subgroup of a quantum group. We suggest a general definition, which takes into account the work that has been done for quantum homogeneous spaces. We further restrict our attention to reductive subgroups,…