Polygroup Theory and Related Systems.:
This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, t...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore :
World Scientific,
2012.
|
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| Summary: | This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics. |
| Physical Description: | 1 online resource (209 pages) |
| Bibliography: | Includes bibliographical references (pages 189-196) and index. |
| ISBN: | 9789814425315 9814425311 |
Staff View
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| 505 | 0 | |a Preface; Contents; 1. A Brief Excursion into Group Theory; 1.1 Introduction; 1.2 The abstract definition of a group and some examples; 1.3 Subgroups; 1.4 Normal subgroups and quotient groups; 1.5 Group homomorphisms; 1.6 Permutation groups; 1.7 Direct product; 1.8 Solvable and nilpotent groups; 2. Hypergroups; 2.1 Introduction and historical development of hypergroups; 2.2 Definition and examples of hypergroups; 2.3 Some kinds of subhypergroups; 2.4 Homomorphisms of hypergroups; 2.5 Regular and strongly regular relations; 2.6 Complete hypergroups; 2.7 Join spaces; 3. Polygroups. | |
| 505 | 8 | |a 3.1 Definition and examples of polygroups3.2 Extension of polygroups by polygroups; 3.3 Subpolygroups and quotient polygroups; 3.4 Isomorphism theorems of polygroups; 3.5 relation on polygroups; 3.6 Generalized permutations; 3.7 Permutation polygroups; 3.8 Representation of polygroups; 3.9 Polygroup hyperrings; 3.10 Solvable polygroups; 3.11 Nilpotent polygroups; 4. Weak Polygroups; 4.1 Weak hyperstructures; 4.2 Weak polygroups as a generalization of polygroups; 4.3 Fundamental relations on weak polygroups; 4.4 Small weak polygroups; 5. Combinatorial Aspects of Polygroups. | |
| 505 | 8 | |a 5.1 Chromatic polygroups5.2 Polygroups derived from cogroups; 5.3 Conjugation lattice; Bibliography; Index. | |
| 520 | |a This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics. | ||
| 588 | 0 | |a Print version record. | |
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| 650 | 0 | |a Hypergroups. |0 http://id.loc.gov/authorities/subjects/sh85063698 | |
| 650 | 6 | |a Théorie des groupes. | |
| 650 | 6 | |a Hypergroupes. | |
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| contents | Preface; Contents; 1. A Brief Excursion into Group Theory; 1.1 Introduction; 1.2 The abstract definition of a group and some examples; 1.3 Subgroups; 1.4 Normal subgroups and quotient groups; 1.5 Group homomorphisms; 1.6 Permutation groups; 1.7 Direct product; 1.8 Solvable and nilpotent groups; 2. Hypergroups; 2.1 Introduction and historical development of hypergroups; 2.2 Definition and examples of hypergroups; 2.3 Some kinds of subhypergroups; 2.4 Homomorphisms of hypergroups; 2.5 Regular and strongly regular relations; 2.6 Complete hypergroups; 2.7 Join spaces; 3. Polygroups. 3.1 Definition and examples of polygroups3.2 Extension of polygroups by polygroups; 3.3 Subpolygroups and quotient polygroups; 3.4 Isomorphism theorems of polygroups; 3.5 relation on polygroups; 3.6 Generalized permutations; 3.7 Permutation polygroups; 3.8 Representation of polygroups; 3.9 Polygroup hyperrings; 3.10 Solvable polygroups; 3.11 Nilpotent polygroups; 4. Weak Polygroups; 4.1 Weak hyperstructures; 4.2 Weak polygroups as a generalization of polygroups; 4.3 Fundamental relations on weak polygroups; 4.4 Small weak polygroups; 5. Combinatorial Aspects of Polygroups. 5.1 Chromatic polygroups5.2 Polygroups derived from cogroups; 5.3 Conjugation lattice; Bibliography; Index. |
| ctrlnum | (OCoLC)827210175 |
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| discipline | Mathematik |
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| indexdate | 2025-04-11T08:41:14Z |
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| spelling | Davvaz, Bijan. Polygroup Theory and Related Systems. Singapore : World Scientific, 2012. 1 online resource (209 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Preface; Contents; 1. A Brief Excursion into Group Theory; 1.1 Introduction; 1.2 The abstract definition of a group and some examples; 1.3 Subgroups; 1.4 Normal subgroups and quotient groups; 1.5 Group homomorphisms; 1.6 Permutation groups; 1.7 Direct product; 1.8 Solvable and nilpotent groups; 2. Hypergroups; 2.1 Introduction and historical development of hypergroups; 2.2 Definition and examples of hypergroups; 2.3 Some kinds of subhypergroups; 2.4 Homomorphisms of hypergroups; 2.5 Regular and strongly regular relations; 2.6 Complete hypergroups; 2.7 Join spaces; 3. Polygroups. 3.1 Definition and examples of polygroups3.2 Extension of polygroups by polygroups; 3.3 Subpolygroups and quotient polygroups; 3.4 Isomorphism theorems of polygroups; 3.5 relation on polygroups; 3.6 Generalized permutations; 3.7 Permutation polygroups; 3.8 Representation of polygroups; 3.9 Polygroup hyperrings; 3.10 Solvable polygroups; 3.11 Nilpotent polygroups; 4. Weak Polygroups; 4.1 Weak hyperstructures; 4.2 Weak polygroups as a generalization of polygroups; 4.3 Fundamental relations on weak polygroups; 4.4 Small weak polygroups; 5. Combinatorial Aspects of Polygroups. 5.1 Chromatic polygroups5.2 Polygroups derived from cogroups; 5.3 Conjugation lattice; Bibliography; Index. This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics. Print version record. Includes bibliographical references (pages 189-196) and index. Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Hypergroups. http://id.loc.gov/authorities/subjects/sh85063698 Théorie des groupes. Hypergroupes. MATHEMATICS Functional Analysis. bisacsh Group theory fast Hypergroups fast has work: Polygroup theory and related systems (Text) https://id.oclc.org/worldcat/entity/E39PCGKmjrmr4pQfGGYG6Jtcpq https://id.oclc.org/worldcat/ontology/hasWork Print version: Davvaz, Bijan. Polygroup Theory and Related Systems. Singapore : World Scientific, ©2012 9789814425308 |
| spellingShingle | Davvaz, Bijan Polygroup Theory and Related Systems. Preface; Contents; 1. A Brief Excursion into Group Theory; 1.1 Introduction; 1.2 The abstract definition of a group and some examples; 1.3 Subgroups; 1.4 Normal subgroups and quotient groups; 1.5 Group homomorphisms; 1.6 Permutation groups; 1.7 Direct product; 1.8 Solvable and nilpotent groups; 2. Hypergroups; 2.1 Introduction and historical development of hypergroups; 2.2 Definition and examples of hypergroups; 2.3 Some kinds of subhypergroups; 2.4 Homomorphisms of hypergroups; 2.5 Regular and strongly regular relations; 2.6 Complete hypergroups; 2.7 Join spaces; 3. Polygroups. 3.1 Definition and examples of polygroups3.2 Extension of polygroups by polygroups; 3.3 Subpolygroups and quotient polygroups; 3.4 Isomorphism theorems of polygroups; 3.5 relation on polygroups; 3.6 Generalized permutations; 3.7 Permutation polygroups; 3.8 Representation of polygroups; 3.9 Polygroup hyperrings; 3.10 Solvable polygroups; 3.11 Nilpotent polygroups; 4. Weak Polygroups; 4.1 Weak hyperstructures; 4.2 Weak polygroups as a generalization of polygroups; 4.3 Fundamental relations on weak polygroups; 4.4 Small weak polygroups; 5. Combinatorial Aspects of Polygroups. 5.1 Chromatic polygroups5.2 Polygroups derived from cogroups; 5.3 Conjugation lattice; Bibliography; Index. Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Hypergroups. http://id.loc.gov/authorities/subjects/sh85063698 Théorie des groupes. Hypergroupes. MATHEMATICS Functional Analysis. bisacsh Group theory fast Hypergroups fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85057512 http://id.loc.gov/authorities/subjects/sh85063698 |
| title | Polygroup Theory and Related Systems. |
| title_auth | Polygroup Theory and Related Systems. |
| title_exact_search | Polygroup Theory and Related Systems. |
| title_full | Polygroup Theory and Related Systems. |
| title_fullStr | Polygroup Theory and Related Systems. |
| title_full_unstemmed | Polygroup Theory and Related Systems. |
| title_short | Polygroup Theory and Related Systems. |
| title_sort | polygroup theory and related systems |
| topic | Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Hypergroups. http://id.loc.gov/authorities/subjects/sh85063698 Théorie des groupes. Hypergroupes. MATHEMATICS Functional Analysis. bisacsh Group theory fast Hypergroups fast |
| topic_facet | Group theory. Hypergroups. Théorie des groupes. Hypergroupes. MATHEMATICS Functional Analysis. Group theory Hypergroups |
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