Soft Subgroups Research Articles

Soft Groups and Characteristic Soft Subgroups

Group theory is the part of mathematics which addresses the study of symmetry. This paper extends the investigation of the soft group theory which Aktaş and Çağman have defined. We study new concepts in the soft group theory such as the center of the soft group, the kernel of soft homomorphism and soft automorphisms with their basic properties. Furthermore, the concept of soft point groups is introduced and the properties of these soft groups are studied. We state the concept of characteristic soft subgroups of a given soft group. Also, some theorems related to this concept are investigated. We study the characteristic soft subgroups of a given soft point group. The characteristic soft subgroups play a significant part in the study of the soft group theory and are useful for understanding the structure of a soft group and its soft automorphisms. As an application of characteristic soft subgroups, they allow us to identify and study important soft subgroups that are preserved under soft automorphisms. Also, practical applications for our theory can be conducted in future work such as the relation with other disciplines in sciences.

An extension of Fermatean b-derived fuzzy soft ternary subgroup

In this paper, an extension of the fermatean uncertainty soft subgroup structures under a norm. Also, the cubic fermatean uncertainty soft ideal structures and fermatean uncertainty multigroup over multi-homomorphism are discussed in detail.

The Algebraic Structures of Q-Complex Neutrosophic Soft Sets Associated with Groups and Subgroups

Groups and subgroups are rich algebraic structures, and both of them depend on binary operations in their work. The discussion of this paper is organized into two parts. In the first part, we define the notion of Qcomplex neutrosophic soft sets (Q-CNSSs) by amalgamating two previous models of Q-complex neutrosophic set (Q-CNS) and soft set (SS) to address the issues of two-dimensionality (two variables) in a universal set under a parametric environment. Subsequently, the relation between Q-CNSSs and Q- neutrosophic soft sets (Q-NSSs) is verified. A basic set theory for this hybrid model is developed. In particular, null Q-CNSS and absolute Q-CNSS are defined. The basic operators of the complement, subset, equality, union and intersection are advanced and their properties are examined. Further, the notions of the homogeneous and completely homogeneous Q-CNSSs are proposed along with some illustrated examples. In part two, we move to study some algebraic structures of this model when we define the notions of Q-complex neutrosophic soft groups (QCNSG) and Q-complex neutrosophic soft subgroups (Q-CNSSG). Then, the relation between Q-CNSG and Q-neutrosophic soft group (Q-NSG) is scrutinized. Moreover, the algebraic properties of the Q-CNSG and Q-CNSSG are discussed and verified. Finally, some theories that show the relationship between the Q-CNSG and the soft group are proposed.

M − N ANTI HOMOMORPHISM OF AN M − N FUZZY SOFT SUBGROUPS AND ITS LEVEL M − N SUBGROUPS

In this paper, we have discussed the concept of M N anti homomor- phism of fuzzy soft subgroups, then we define the M N anti level subsets of a fuzzy soft subgroup and its some elementary properties are also discussed.

Fuzzy Soft Groups Based on Fuzzy Space

In this paper, a new theory of fuzzy soft groups (FSG) based on fuzzy spaces (FS) from Dib’s point of view is found. The concept of FSG and fuzzy soft subgroup (FSSG) based on FS was elaborated. The relationship between FSG and FSG is also investigated.

Normal Bipolar Soft Subgroups

In this study, we introduce the concept of normal bipolar soft subgroup and investigate some properties of normal bipolar soft subgroups. We also define notions of bipolar soft left and right cosets of a bipolar soft group and the concept of conjugate bipolar soft subgroup, and obtain some of their properties.

On fundamental isomorphism theorems in soft subgroups

Molodsov initiated a novel concept of soft set theory, which is a completely new approach for modeling vagueness and uncertainty, which there is no limited condition to description of objects and is free from the difficulties affecting existing methods. This makes the theory very convenient and easy to apply in practice. After the pioneering work of Molodsov, there has been a great effort to obtain soft set analogues of classical theories. Among other fields, a progressive developments are made in the field of algebraic structure. To extend the soft set in group theory, many researchers introduced the notions of soft subgroup and investigated its applications in group theory and decision making. In this paper, by using the soft sets and their duality, we introduce new concepts on the soft sets, which are called soft quotient subgroup and quotient dual soft subgroup. We then derive their algebraic properties and, in sequel, investigate the fundamental isomorphism theorems in soft subgroups analogous to the group theory.

GP-Fuzzy Soft Groups

In this paper, the definition of a new concept which is called GP-fuzzy soft subgroup is introduced and some basic properties of the families of GP-fuzzy soft subgroups are examined.

M-N Fuzzy Normal Soft Groups

In this paper, we have discussed the concept of M-N fuzzy normal soft group, we then define the M-N level subsets of a fuzzy normal soft subgroup and its some elementary properties are also discussed. The presented method in this manuscript is more sensible and also reliable in solving the problems. This method can solve the decision making problems

Some Elementary Combinatorial Properties of Aktas' Soft Groups with Contributions in Soft Actions

As a generic mathematical tool, the concept of soft sets introduced in 1999 by Molodtesov, and in continuation of this research the soft groups defined and studied for their nice properties by Aktas in 2007. Because of the extensive applications of soft sets and soft groups in all branches of sciences involving mathematics we prefer to concentrate on the algebraic properties of algebraic structures. The action of groups on sets is an effective instrument in algebra. In this note we drive some basic combinatorial properties of soft groups using Aktas's definition of soft group and soft subgroups. By giving the definition of soft actions of groups and semigroups we managed to exhibit their congruence properties in this paper.

A novel approach: soft groups

In this paper, we construct a soft group and soft subgroups by assigning a group structure to the universe set X and investigate some interesting results in this context.

ON (m, n) –Upper Q-Fuzzy Soft Subgroups

In this paper we shall study some properties for upper Q- fuzzy subgroups, some lemma and theorem for this subject. We shall study the upper Q- fuzzy index with the upper fuzzy sub groups; also we shall give some new definitions for this subject. On the other hand we shall give the definition of the upper normal fuzzy subgroups, and study the main theorem for this. We shall also give new results on this subject.

English

In this paper, we introduce the concept of normal fuzzy soft group. We also define the level subsets of a normal fuzzy soft subgroup and discussed some of its properties.

Soft Neutrosophic Bigroup and Soft Neutrosophic N-Group

Soft neutrosophic group and soft neutrosophic subgroup are generalized to soft neutrosophic bigroup and soft neutrosophic N-group respectively in this paper. Different kinds of soft neutrosophic bigroup and soft neutrosophic N-group are given. The structural properties and theorems have been discussed with a lot of examples to disclose many aspects of this beautiful man made structure.

Study on Soft Groups

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, we further study the properties of soft sets and their duality. Moreover, we introduce the new concepts of soft subgroups and normal soft subgroups of a group. Some algebraic properties about soft subgroups and normal soft subgroups are investigated.

On the soft sets and algebraic structures

The main purpose of this study is to introduce and investigate the basic concepts of soft set theory and soft group theory. We give some examples for the soft groups and soft subgroups. Mathematics Subject Classification: 06D72, 03G25

Some further properties of soft subgroups

A subgroup H of a p-group G is n-uniserial if for each i = 1, . . . , n, there is a unique subgroup Ki such that H≤Ki and |Ki : H | = pi. In case the subgroups of G containing H form a chain we say that H is uniserially embedded in G. We prove that if p is odd and that K is a 2-uniserial subgroup of order p in the p-group G. Then K is uniserially embedded in G. We also show that for p > 3, if K is a 2-uniserial cyclic subgroup of the p-group G, then K is uniserially embedded in G. We prove the following two theorems : (1) Let A be a soft subgroup of index greater than p. Let N1 = NG (A) and R = G'Z (N1). Then the A-invariant subgroups of R containing Z (N1) form a chain. (2) Suppose that the p-group G has a uniserially embedded subgroup P of order p. Then either G has a cyclic subgroup of index p or is of maximal class (coclass 1).

On Subgroups of p -Groups Having Soft Subgroups

On Subgroups of <i>p</i> -Groups Having Soft Subgroups