Lattice-ordered loops and quasigroups

Right Product Quasigroups and Loops

Right groups are direct products of right zero semigroups and groups and they play a significant role in the semilattice decomposition theory of semigroups. Right groups can be characterized as associative right quasigroups (magmas in which left translations are bijective). If we do not assume associativity we get right quasigroups which are not necessarily representable as direct products of r...

Small Latin Squares, Quasigroups and Loops

We present the numbers of isotopy classes and main classes of Latin squares, and the numbers of isomorphism classes of quasigroups and loops, up to order 10. The best previous results were for Latin squares of order 8 (Kolesova, Lam and Thiel, 1990), quasigroups of order 6 (Bower, 2000) and loops of order 7 (Brant and Mullen, 1985). The loops of order 8 have been independently found by “QSCGZ” ...

Isotopy Theory Of Smarandache : Quasigroups And Loops ∗ †

The concept of Smarandache isotopy is introduced and its study is explored for Smarandache: groupoids, quasigroups and loops just like the study of isotopy theory was carried out for groupoids, quasigroups and loops. The exploration includes: Smarandache; isotopy and isomorphy classes, Smarandache f, g principal isotopes and G-Smarandache loops.

Computing with quasigroups and loops in GAP

On check character systems over quasigroups and loops

In this article we study check character systems that is error detecting codes, which arise by appending a check digit an to every word a1a2...an−1 : a1a2...an−1 → a1a2...an−1an with the check formula (...((a1 · δa2) · δ 2a3)...) · δ n−2an−1) · δ n−1an = c, where Q(·) is a quasigroup or a loop, δ is a permutation of Q, c ∈ Q. We consider detection sets for such errors as transpositions (ab → ba...