FUZZY MEALY MACHINES: HOMOMORPHISMS, ADMISSIBLE RELATIONS AND MINIMAL MACHINES

1996 ◽  
Vol 04 (01) ◽  
pp. 27-43 ◽  
Author(s):  
J.N. MORDESON ◽  
P.S. NAIR
Keyword(s):  
Group Theory ◽  
Fundamental Theorem ◽  
Existence And Uniqueness ◽  
Normal Subgroups

Homomorphisms and admissible relations of fuzzy Mealy machines are studied. Admissible relations play a role similar to normal subgroups in group theory. The kernel of a homomorphism is shown to be an admissible relation. Conversely, corresponding to an admissible relation, there exists a homomorphism. The fundamental theorem on homomorphisms; and the existence and uniqueness of minimal machines are also presented.

scholarly journals l-simple lattice-ordered groups

1974 ◽  
Vol 19 (2) ◽  
pp. 133-138 ◽  
Author(s):  
A. M. W. Glass
Keyword(s):  
Group Theory ◽  
Lattice Ordered Group ◽  
Normal Subgroups ◽  
Ordered Group ◽  
Central Task ◽  
Ordered Groups ◽  
Simple Lattice ◽  
Lattice Ordered Groups ◽  
Group Play

Let G be a lattice-ordered group (l-group) and H a subgroup of G. H is said to be an l-subgroup of G if it is a sublattice of G. H is said to be convex if h1, h2 ∈ H and h2 ≦ g ≦ h2 imply g ∈ H. The normal convex l-subgroups (l-ideals) of an l-group play the same role in the study of lattice-ordered groups as do normal subgroups in the investigation of groups. For this reason, an l-group is said to be l-simple if it has no non-trivial l-ideals. As in group theory, a central task in the examination of lattice-ordered groups is to characterise those l-groups which are l-simple.

On normal subgroups with consecutive G-class sizes

2016 ◽  
Vol 15 (08) ◽  
pp. 1650151
Author(s):  
Changguo Shao ◽  
Qinhui Jiang
Keyword(s):  
Group Theory ◽  
Normal Subgroup ◽  
Conjugacy Class ◽  
Frobenius Group ◽  
Normal Subgroups ◽  
Conjugacy Class Sizes ◽  
Abelian Kernel ◽  
Consecutive Integers ◽  
Normal Formula

Let [Formula: see text] be a group and [Formula: see text] be a normal subgroup of [Formula: see text]. If the set [Formula: see text] is composed by consecutive integers, then [Formula: see text] is either nilpotent or a quasi-Frobenius group with abelian kernel and complements. This is a generalization of Theorem 2 of [A. Beltrán, M. J. Felipe and C. G. Shao, [Formula: see text]-divisibility of conjugacy class sizes and normal [Formula: see text]-complements, J. Group Theory 18 (2015) 133–141].

Groups

2017 ◽  
Author(s):  
Matt Clay ◽  
Dan Margalit
Keyword(s):  
Group Theory ◽  
Electric Field ◽  
Geometric Group Theory ◽  
Normal Subgroups ◽  
Infinite Groups ◽  
Higher Dimensional ◽  
Group Presentations ◽  
Planar Shape ◽  
Group Of Symmetries

This chapter considers the notion of a group in mathematics. It begins with a discussion of the problem of determining the symmetry of an object such as a planar shape, a higher-dimensional solid, a group, or an electric field. It then describes every group as a group of symmetries of some object and shows what it means for a group to be a group of symmetries of an object. These ideas are at the very heart of geometric group theory, the study of groups, spaces, and the interactions between them. The chapter also examines infinite groups, homomorphisms and normal subgroups, and group presentations. A number of exercises are included.

COMPONENTS AND MINIMAL NORMAL SUBGROUPS OF FINITE AND PSEUDOFINITE GROUPS

2019 ◽  
Vol 84 (1) ◽  
pp. 290-300
Author(s):  
JOHN S. WILSON
Keyword(s):  
Finite Group ◽  
Group Theory ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Minimal Normal Subgroup ◽  
Normal Subgroups ◽  
First Order ◽  
Order Language ◽  
Image Position ◽  
A Finite Group

AbstractIt is proved that there is a formula$\pi \left( {h,x} \right)$in the first-order language of group theory such that each component and each non-abelian minimal normal subgroup of a finite groupGis definable by$\pi \left( {h,x} \right)$for a suitable elementhofG; in other words, each such subgroup has the form$\left\{ {x|x\pi \left( {h,x} \right)} \right\}$for someh. A number of consequences for infinite models of the theory of finite groups are described.

EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE DISCRETIZED CONTACT ELASTO-PLASTIC PROBLEM WITH ISOTROPIC HARDENING

2000 ◽  
Vol 10 (08) ◽  
pp. 1151-1179 ◽  
Author(s):  
EDUARD ROHAN
Keyword(s):  
Variational Inequalities ◽  
Fundamental Theorem ◽  
Existence And Uniqueness ◽  
Contact Problems ◽  
Isotropic Hardening ◽  
Plastic Strains ◽  
Uniqueness Of Solutions ◽  
Operator Equations

A class of quasistatic contact problems for elasto-plastic bodies with isotropic hardening is considered. The problems involve displacements, plastic strains and plastic multipliers. In the framework of multi-valued operator equations, the existence and uniqueness assertions for discretized reduced subproblems are proved using a fundamental theorem on variational inequalities.

Born geometry on ρ-commutative algebra

2020 ◽  
Vol 17 (14) ◽  
pp. 2050210
Author(s):  
Zahra Bagheri ◽  
Esmaeil Peyghan
Keyword(s):  
Commutative Algebra ◽  
Riemannian Geometry ◽  
Fundamental Theorem ◽  
Existence And Uniqueness ◽  
Commutative Algebras

The aim of this paper is to establish a generalization of the Born geometry to [Formula: see text]-commutative algebras. We introduce the notion of Born [Formula: see text]-commutative algebras and study the existence and uniqueness of a torsion connection which preserves the Born structure. Also, an analogue of the fundamental theorem of Riemannian geometry will be proved for these algebras.

scholarly journals Tópicos de Teoria dos Grupos nos cursos de licenciatura em Matemática

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
NATÁLIA COELHO SOARES ◽  
BARBARA LUTAIF BIANCHINI
Keyword(s):  
Group Theory ◽  
Teacher Training ◽  
Mathematics Teacher ◽  
Normal Subgroups ◽  
Qualitative Character ◽  
Finite Abelian Groups ◽  
Structured Interviews ◽  
Cyclic Groups ◽  
Doctoral Research ◽  
Quotient Groups

ResumoEste trabalho apresenta parte de uma pesquisa de doutorado em andamento que tem por objetivo investigar quais tópicos da Teoria dos Grupos são imprescindíveis na formação do licenciando em matemática. A pesquisa tem cunho qualitativo, na qual são realizadas entrevistas semiestruturadas com especialistas em Teoria de Grupos, educadores matemáticos envolvidos em educação algébrica e com professores da disciplina em cursos de Licenciatura em Matemática. Neste texto apresentamos os resultados obtidos em duas entrevistas. Os entrevistados concordam que definição de grupo, subgrupos, grupos cíclicos, homomorfismo e isomorfismo de grupos, grupo de permutações, classes laterais, subgrupos normais, grupos abelianos finitos, grupo de transformações no plano e no espaço, grupos quocientes são conteúdos imprescindíveis em um curso de licenciatura. Palavras-Chave: Teoria dos Grupos; Licenciatura em Matemática; Formação de professores.AbstractThis paper presents part of a doctoral research in progress that aims to investigate which topics of group theory are essential in the formation of the graduate in mathematics. The research has a qualitative character, in which semi-structured interviews are conducted with specialists in group theory, mathematical educators involved in algebraic education and with professors of the discipline in undergraduate courses in mathematics. In this text we present the results obtained in two interviews. Interviewees agree that group definition, subgroups, cyclic groups, homomorphism and isomorphism of groups, permutations group, side classes, normal subgroups, finite abelian groups, group of transformations in the plane and space, quotient groups are essential content in a course of degree.Keywords: Group Theory; Degree in Mathematics; Teacher training. 

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