Polygroup Theory and Related Systems

Nonfiction, Science & Nature, Mathematics, Combinatorics, Algebra
Cover of the book Polygroup Theory and Related Systems by Bijan Davvaz, World Scientific Publishing Company
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Author: Bijan Davvaz ISBN: 9789814425322
Publisher: World Scientific Publishing Company Publication: September 28, 2012
Imprint: WSPC Language: English
Author: Bijan Davvaz
ISBN: 9789814425322
Publisher: World Scientific Publishing Company
Publication: September 28, 2012
Imprint: WSPC
Language: English

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.

Contents:

  • A Brief Excursion into Group Theory:

    • Introduction
    • The Abstract Definition of a Group and Some Examples
    • Subgroups
    • Normal Subgroups and Quotient Groups
    • Group Homomorphisms
    • Permutation Groups
    • Direct Product
    • Solvable and Nilpotent Groups
  • Hypergroups:

    • Introduction and Historical Development of Hypergroups
    • Definitions and Examples of Hypergroups
    • Some Kinds of Subhypergroups
    • Homomorphisms of Hypergroups
    • Regular and Strongly Regular Relations
    • Complete Hypergroups
    • Join Spaces
  • Polygroups:

    • Definition and Examples of Polygroups
    • Extension of Polygroups by Polygroups
    • Subpolygroups and Quotient Polygroups
    • Isomorphism Theorems of Polygroups
    • γ* Relation on Polygroups
    • Generalized Permutations
    • Permutation Polygroups
    • Representation of Polygroups
    • Polygroup Hyperrings
    • Solvable Polygroups
    • Nilpotent Polygroups
  • Weak Polygroups:

    • Weak Hyperstructures
    • Weak Polygroups as a Generalization of Polygroups
    • Fundamental Relations on Weak Polygroups
    • Small Weak Polygroups
  • Combinatorial Aspects of Polygroups:

    • Chromatic Polygroups
    • Polygroups Derived from Cogroups
    • Conjugation Lattice

Readership: Graduate students and researchers in algebraic hyperstructures and applications.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

Contents:

Readership: Graduate students and researchers in algebraic hyperstructures and applications.

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