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Polygroup Theory and Related System by Bijaan Davvaz

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Polygroup Theory and Related System written by Bijaan Davvaz . This is an other great mathematics book cover the following topics.

  • 1. A Brief Excursion into Group Theory
    1.1 Introduction
    1.2 The abstract de nition 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 De nition 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 De nition and examples of polygroups
    3.2 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 polygroups
    5.2 Polygroups derived from cogroups
    5.3 Conjugation lattice

  • Bibliography

  • Index

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