74 citations
- Wabash CollegeUS2 papers
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5 papers · 1 filter
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 quasigroups of Bol-Moufang type: An equational reasoning approach
J. D. Phillips, Petr Vojtěchovský
A quasigroup 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, the order in which the variables a…
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…
Toward the classification of Moufang loops of order 64
Petr Vojtěchovský
We show how to obtain all nonassociative Moufang loops of order less than 64 and 4262 nonassociative Moufang loops of order 64 in a unified way. We conjecture that there are no oth…
The smallest Moufang loop revisited
Petr Vojtěchovský
We derive presentations for Moufang loops of type , defined by Chein, with finite, two-generated. We then use to visualize the smallest non-associative Moufang…