Almost all quasigroups have rank 2

DOI10.1016/0012-365X(92)90537-PzbMath0786.20041MaRDI QIDQ1199589

Peter J. Cameron

Publication date: 16 January 1993

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetric groupquasigroupalternating groupmultiplication tablemultiplication groupgroup of permutationsnumber of Latin squaresnumber of quasigroupsvan der Waerden permanent conjecture

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Asymptotic results on counting functions for algebraic and topological structures (11N45) Orthogonal arrays, Latin squares, Room squares (05B15) Loops, quasigroups (20N05) Subgroups of symmetric groups (20B35) Multiply transitive finite groups (20B20)

Related Items

Random Permutations: Some Group-Theoretic Aspects, On Random Generation of the Symmetric Group, A theorem on random matrices and some applications, All-even Latin squares, Large deviations in random latin squares, Unnamed Item, On the smallest simple, unipotent Bol loop., Strong polynomial completeness of almost all quasigroups

Cites Work

• Unnamed Item
• Characters of finite quasigroups. III: Quotients and fusion
• Notes on Egoritsjev's proof of the van der Waerden conjecture
• Proof of the van der Waerden conjecture regarding the permanent of a doubly stochastic matrix
• The solution of van der Waerden's problem for permanents
• On the order of uniprimitive permutation groups
• Finite Permutation Groups and Finite Simple Groups
• Centraliser rings of multiplication groups on quasigroups
• The probability of generating the symmetric group