Rectangular loops and rectangular quasigroups

Details Rectangular loops and rectangular quasigroups Rectangular loops and rectangular quasigroups

2004-09-05

arxiv.org/abs/math/0409074v3

Comput. Math. Appl. 49 (2005), no. 11-12, 1679--1685.

Mathematics

Group Theory

5 pages, AMS-LaTeX; v.2: minor corrections of proofs; v.3: added section discussing use of automated reasoning, other minor ch

Scientific paper

We solve two problems posed by Krape\v{z} by finding a basis of seven independent axioms for the variety of rectangular loops. Six of these axioms form a basis for the variety of rectangular quasigroups. The proofs of the lemmas showing that the six axioms are sufficient are based on proofs generated by the automated reasoning program OTTER, while most of the models verifying the independence of the axioms were generated by the finite model builder Mace4.

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