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    Polygroup Theory and Related Systems:

    ISBN-10: 9814425303
    ISBN-13: 9789814425308
    Edition: 2012
    Author(s): Bijan Davvaz
    Description: "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  More...
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    List Price: $44.00
    Copyright Year: 2012
    Publisher: World Scientific Pub Co Inc
    Binding: Cloth Text 
    Pages: 200
    Size: 6.00" wide x 9.00" long x 1.00" tall
    Weight: 1.188
    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."--Publisher's website.

    Preface
    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
    Definition 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
    �* relation on polygroups
    Generalized permutations
    Permutation polygroups
    Representation of polygroups
    Polygroup hyper rings
    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
    Bibliography
    Index

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