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A CHARACTERIZATION OF FINITE BILINEAR QUASIGROUPS
Keywords:
groupoid, quasigroup, order of a quasigroup, Cayley tableDOI:
https://doi.org/10.17654/0972087124009Abstract
The study of finite quasigroups is reduced to primary quasigroups, since each finite quasigroup is isomorphic to a product of primary quasigroups. Afterward, we characterize primary bilinear quasigroups, and propose an algorithm to decide whether any primary quasigroup given by one of its Cayley tables is bilinear. Also, we determine corresponding bilinear polynomials, if there be.
Received: January 21, 2024
Revised: March 28, 2024
Accepted: April 5, 2024
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