Polyadic Groups

Polyadic Groups

多元组
应用数学

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作者

Dudek Wieslaw A.||

出版社

CRC Press

出版时间

2024年03月22日

装帧

精装

ＩＳＢＮ

9781032697246

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页码

408

开本

234 x 156 mm (6.14 x 9.21

语种

英文

版次

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图书简介

This book provides a general, unified approach to the theory of polyadic groups, their normal subgroups and matrix representations.The author focuses on those properties of polyadic groups which are not present in the binary case. These properties indicate a strong relationship between polyadic groups and various group-like algebras, as well as ternary Hopf algebras and n-Lie algebras that are widely used in theoretical physics.The relationships of polyadic groups with special types of binary groups, called covering groups and binary retracts, are described. These relationships allow the study of polyadic groups using these binary groups and their automorphisms.The book also describes the affine geometry induced by polyadic groups and fuzzy subsets defined on polyadic groups. Finally, we discuss the categories of polyadic groups and the relationships between the different varieties of polyadic groups. In many cases, we give elegant new proofs of known theorems. We also give many interesting examples and applications.The book contains many little-known results from articles previously published in hard-to-reach Russian, Ukrainian and Macedonian journals. These articles are not in English.

Preface Introduction 1. Basic concepts 1.1 Basic definitions and examples 1.2 Homomorphisms 1.3 Covering semigroups 1.4 Extension of homomorphisms 1.5 Post’s coset theorem 1.6 Cancellable elements 1.7 Regular $n$-semigroups 1.8 Inverse $n$-semigroups 1.9 Divisibility in $n$-semigroups 1.10 Retracts 1.11 Notes on Chapter 1 2. Varieties of $n$-groups 2.1 D\"ornte’s identities 2.2 Generalized D\"ornte’s identities 2.3 Variety of $n$-groups 2.4 Subvariety of idempotent $n$-groups 2.5 Free $n$-groups 2.6 Notes on Chapter 2 3 Partially commutative $n$-groups 3.1 Binary quasigroups 3.2 Medial $n$-quasigroups 3.3 Medial $n$-groups 3.4 Permutable $n$-groups 3.5 $m$-semiabelian $n$-groups 3.6 Weakly semiabelian $n$-groups 3.7 Free semiabelian $n$-groups 3.8 Notes on Chapter 3 4 Subgroups 4.1 Normal $n$-subgroups 4.2 Normalizers and seminormalizers 4.3 Congruences 4.4 Nilpotent $n$-groups 4.5 Direct products of $n$-groups 4.6 Rusakov’s direct product 4.7 Notes on Chapter 4

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