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Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups
Kenneth W. Johnson, Petr Vojtěchovský
The variety of quasigroups satisfying the identity mirrors the variety of groups, and offers a new look at groups and their multiplication tables. Such quasigroups ar…
The varieties of loops of Bol-Moufang type
J. D. Phillips, Petr Vojtěchovský
A loop identity is of Bol-Moufang type if two of its three variables occur once on each side, the third variable occurs twice on each side, and the order in which the variables app…
Linear groupoids and the associated wreath products
J. D. Phillips, Petr Vojtěchovský
A groupoid identity is said to be linear of length if the same variables appear on both sides of the identity exactly once. We classify and count all varieties of groupoid…
Combinatorial polarization, code loops, and codes of high level
Petr Vojtěchovský
We first find the combinatorial degree of any map where is a finite field and is a finite-dimensional vector space over . We then simplify and generalize a ce…
Reconstruction of group multiplication tables by quadrangle criterion
Petr Vojtěchovský
For , every partial Cayley matrix with at most holes can be reconstructed by quadrangle criterion. Moreover, the holes can be filled in given order. Without…