Introduction to Quasigroups and Their Representations
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A01=Jonathan D. H. Smith
abelian
Abelian Group
advanced quasigroup representation theory
algebraic combinatorics
Author_Jonathan D. H. Smith
Bose Mesner Algebra
Category=PBG
Central Congruence
Character Table
Coalgebra Homomorphism
combinatorial algebra
Conjugacy Class
cryptography mathematics
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
finite
Finite Quasigroup
Homogeneous Space
Homomorphic Image
Idempotent Quasigroup
Incidence Matrix
Lagrange Property
loop
Loop Transversal
Markov Matrix
mathematical structures
module theory applications
moufang
Moufang Loop
nonempty
Nonempty Quasigroup
Normal Subgroup
Partial Latin Square
Permutation Character
Permutation Representation
steiner
Steiner Triple System
Symmetric Group S3
system
systems
Tensor Square
Transitive Permutation Representation
transversal
triple
universal algebra concepts
Universal Stabilizer
Product details
- ISBN 9781584885375
- Weight: 810g
- Dimensions: 156 x 234mm
- Publication Date: 15 Nov 2006
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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.
