# An Introduction to Quasigroups and Their Representations

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Collecting results scattered throughout the literature into one source, An Introduction to Quasigroups and Their Representations shows how representation theories for groups are capable of extending to general quasigroups and illustrates the added depth and richness that result from this extension.To fully understand representation theory, the first three chapters provide a foundation in the theory of quasigroups and loops, covering special classes, the combinatorial multiplication group, universal stabilizers, and quasigroup analogues of abelian groups. Subsequent chapters deal with the three main branches of representation theory-permutation representations of quasigroups, combinatorial character theory, and quasigroup module theory. Each chapter includes exercises and examples to demonstrate how the theories discussed relate to practical applications. The book concludes with appendices that summarize some essential topics from category theory, universal algebra, and coalgebras.

Long overshadowed by general group theory, quasigroups have become increasingly important in combinatorics, cryptography, algebra, and physics. Covering key research problems, An Introduction to Quasigroups and Their Representations proves that you can apply group representation theories to quasigroups as well. less

CRC Press; November 2006

353 pages; ISBN 9781420010633

Read online, or download in secure PDF format

Title: An Introduction to Quasigroups and Their Representations

Author: Jonathan D. H. Smith

353 pages; ISBN 9781420010633

Read online, or download in secure PDF format

Title: An Introduction to Quasigroups and Their Representations

Author: Jonathan D. H. Smith

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Subject categories

- Academic > Mathematics > Algebra > Quasigroups
- Academic > Mathematics > General > Vinogradov, Ivan Matveevich, 1891-
- Academic > Mathematics > General > Mathematics; Periodicals
- Academic > Mathematics > General > Mathematics; Study and teaching; Audio-visual aids
- Mathematics > Algebra
- Mathematics > Number Theory

ISBNs

1420010638

9781420010633

9781584885375