Maximal and Frattini L-subgroups of an L-group

I. Jahan; A. Manas

doi:10.3233/jifs-200157

Maximal and Frattini L-subgroups of an L-group

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-200157 ◽

2020 ◽

Vol 39 (3) ◽

pp. 3995-4007

Author(s):

I. Jahan ◽

A. Manas

Keyword(s):

Group Theory ◽

Classical Group

In this paper, the concept of a maximal L-subgroup of an L-group has been defined in the spirit of classical group theory. Then, a level subset characterization has been established for the same. Then, this notion of maximal L-subgroups has been used to define Frattini L-subgroup. Further, the concept of non-generators of an L-group has been developed and its relation with the Frattini L-subgroup of an L-group has been established like their classical counterparts. Moreover, several properties pertaining to the concepts of maximal L-subgroups and Frattini L-subgroup have also been investigated. These two notions have been illustrated through several examples.

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Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

Symmetry ◽

10.3390/sym10080321 ◽

2018 ◽

Vol 10 (8) ◽

pp. 321 ◽

Cited By ~ 4

Author(s):

Mehmet Çelik ◽

Moges Shalla ◽

Necati Olgun

Keyword(s):

Group Theory ◽

Significant Role ◽

Classical Group ◽

Algebraic Structures ◽

Algebraic Systems ◽

Homomorphism Theorem ◽

Special Cases ◽

Isomorphism Theorems

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

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Some Group Theoretic Notions in Fuzzy Multigroup Context

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-7998-0190-0.ch003 ◽

2020 ◽

pp. 34-62 ◽

Cited By ~ 1

Author(s):

Paul Augustine Ejegwa

Keyword(s):

Group Theory ◽

Direct Product ◽

Classical Group ◽

The Relationship ◽

Product Of Groups

The notion of fuzzy multigroups is an application of fuzzy multisets or fuzzy bags to classical group theory. This chapter explores the notions of fuzzy comultisets, characteristic fuzzy submultigroups, and direct product of fuzzy multigroups as extensions of cosets, characteristic subgroups, and direct product of groups. The relationship between fuzzy comultisets of a fuzzy multigroup and the cosets of a group is established. Some results on the concept of fuzzy comultisets are deduced. A number of properties of characteristic fuzzy submultigroups of fuzzy multigroups are outlined, and some related results are obtained. Also, the author presents some properties of direct product of fuzzy multigroups and establish some results.

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Neutrosophic Multigroup Homomorphism and Some of its Properties

10.54216/ijns.170203 ◽

2021 ◽

pp. 110-126

Author(s):

Memet Sahin ◽

Keyword(s):

Group Theory ◽

Set Theory ◽

Homomorphic Image ◽

Fuzzy Set ◽

Algebraic Structure ◽

Fuzzy Set Theory ◽

Classical Group ◽

Elementary Theory ◽

Group Structure ◽

Basic Properties

In a way, the notion of neutrosophic multigroup is an application of neutrosophic multisets to the theory of group. The concept of neutrosophic multigroup is an algebraic structure of neutrosophic multiset that generalizes both the theories of classical group and neutrosophic group. Neutrosophic multigroup constitutes an application of neutrosophic multiset to the elementary theory of classical group. In this paper, we propose the concept of homomorphism on neutrosophic multigroup. We define homomorphism kerlf, automorphism, homomorphic image and homomorphic preimage of neutrosophic multigroup, respectively. Some homomorphic properties of neutrosophic multigroup are explicated. Some homomorphic properties of neutrosophic multigroup are also discussed. This new concept of homomorphism as a bridge among set theory, fuzzy set theory, neutrosophic multiset theory and group theory and also shows the effect of neutrosophic multisets on a group structure. We finally derive the basic properties of neutrosophic multigroup homomorphism and give its applications to group theory

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Classical group theory adapted to the mechanism of Pt3Ni nanoparticle growth: the role of W(CO)6 as the “shape-controlling” agent

Physical Chemistry Chemical Physics ◽

10.1039/c5cp05060j ◽

2016 ◽

Vol 18 (1) ◽

pp. 75-78

Author(s):

M. Radtke ◽

A. Ignaszak

Keyword(s):

Thermal Decomposition ◽

Group Theory ◽

Crystal Growth ◽

Classical Group ◽

Metal Carbonyl ◽

Nanoparticle Growth ◽

Epitaxial Crystal Growth ◽

Shape Controlling

The transition of Pt3Ni cubes into cuboctahedral structures proceeds via epitaxial crystal growth over the metal carbonyl template below the thermal decomposition of W(CO)6.

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