Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423415 | Discrete Mathematics | 2013 | 10 Pages |
Abstract
The quasivariety of groupoids (N,â) satisfying the implication aâb=câdâaâd=câb=aâb generalises rectangular semigroups and central groupoids. We call them rectangular groupoids and find three combinatorial structures based upon arrays, matrices and graphs that are closely related.These generalise several groupoids of independent interest. The quasivariety generates the variety of all groupoids; they satisfy no nontrivial equations. We see some strong connections with isotopy, this being one of the classes of algebras (along with quasigroups) closed under isotopy. We investigate some constructions and show that a regular automorphism exists iff the groupoid is derived from a group via a Cayley graph construction.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Tim Boykett,