1 QUASIGROUPS AND LOOPS
1.1 Latin squares
1.2 Equational quasigroups
1.3 Conjugates
1.4 Semisymmetry and homotopy
1.5 Loops and piques
1.6 Steiner triple systems I
1.7 Moufang loops and octonions
1.8 Triality
1.9 Normal forms
1.10 Exercises
1.11 Notes
2 MULTIPLICATION GROUPS
2.1 Combinatorial multiplication groups
2.2 Surjections
2.3 The diagonal action
2.4 Inner multiplication groups of piques
2.5 Loop transversals and right quasigroups
2.6 Loop transversal codes
2.7 Universal multiplication groups
2.8 Universal stabilizers
2.9 Exercises
2.10 Notes
3 CENTRAL QUASIGROUPS
3.1 Quasigroup congruences
3.2 Centrality
3.3 Nilpotence
3.4 Central isotopy
3.5 Central piques
3.6 Central quasigroups
3.7 Quasigroups of prime order
3.8 Stability congruences
3.9 No-go theorems
3.10 Exercises
3.11 Notes
4 HOMOGENEOUS SPACES
4.1 Quasigroup homogeneous spaces
4.2 Approximate symmetry
4.3 Macroscopic symmetry
4.4 Regularity
4.5 Lagrangean prcperties
4.6 Exercises
4.7 Notes
5 PERMUTATION REPRESENTATIONS
5.1 The category ]FSQ
5.2 Actions as coalgebras
5.3 Irreducibility
5.4 The covariety of Q-sets
5.5 The Burnside algebra
5.6 An example
5.7 Idempotents
5.8 Burnside's Lemma
5.9 Exercises
5.10 Problems
5.11 Notes
6 CHARACTER TABLES
6.1 Conjugacy classes
6.2 Class functions
6.3 The centralizer ring
6.4 Convolution of class functions
6.5 Bose-Mcsner and Hecke algebras
6.6 Quasigroup character tables
6.7 Orthogonality relations
6.8 Rank two quasigroups
6.9 Entropy
6.10 Exercises
6.11 Problems
6.12 Netcs
7 COMBINATORIAL CHARACTER THEORY
7.1 Congruence lattices
7.2 Quotients
7.3 Fusion
7.4 Induction
7.5 Linear characters
7.6 Exercises
7.7 Problems
7.8 Notes
8 SCHEMES AND SUPERSCHEMES
8.1 Sharp transitivity
8.2 More no-go theorems
8.3 Superschemes
8.4 Superalgebras
8.5 Tenser squales
8.6 Relation algebras
8.7 The Reconstruction Theorem
8.8 Exercises
8.9 Problems
8.10 Notes
9 PERMUTATION CHARACTERS
9.1 Enveloping algebras
9.2 Structure of enveloping algebras
9.3 The canonical representaticn
9.4 Commutative actions
9.5 Faithful homogeneous spaces
9.6 Characters of homogeneous spaces
9.7 General permutation characters
9.8 The Ising model
9.9 ExeI cises
9.10 Problems
9.11 Nctes
10 MODULES
10.1 Abelian groups and slice categories
10.2 Quasigroup modules
10.3 The Fundamental Theorem
10.4 Differential calculus
10.5 Representations in varieties
10.6 Group representations
10.7 Exercises
10.8 Problems
10.9 Notes
11 APPLICATIONS OF MODULE THEORY
11.1 Nonassociative lowers
11.2 Exponents
11.3 Steincr triple systems Ⅱ
11.4 The Burrside Problem
11.5 A free commutative Mcufang loop
11.6 Extensions aid cohomology
11.7 Exercises
11.8 Problems
11.9 Notes
12 ANALYTICAL CHARACTER THEORY
12.1 Functions on finite quasigroups
12.2 Periodic functions on groups
12.3 Analytical character theory
12.4 Ahnost periodic functions
12.5 Twisted translation operators
12.6 Proof of the Existence Theorem
12.7 Exercises
12.8 Problems
12.9 Notes
A CATEGORICAL CONCEPTS
A.1 Graphs and categories
A.2 Natural transformations and functors
A.3 Limits and colimits
B UNIVERSAL ALGEBRA
B.1 Combinatorial universal algebra
B.2 Categorical universal algebra
C COALGEBRAS
C.1 Coalgebras and covarieties
C.2 Set functors
References
Index
本书介绍了群表示理论是如何应用到一般的拟群中的，并阐述了其扩展结果的深刻性和丰富性，以及在一般群论的背景之下，拟群在组合数学、密码学、代数学以及物理学中的作用是如何变得越来越重要的。本书共包含十二章及三个附录，为了充分阐述表示理论，前三章为拟群和圈的理论提供了基础，包括拉丁方、组合乘法群、万有稳定化子和中心拟群等，后九章介绍了齐性空间、置换表示、特征标表、组合特征标理论、概型与超概型、置换特征标、模、模理论的应用和解析特征标理论等内容。
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