Principal Loop-Isotopes of Quasigroups

Abstract

If a quasigroup (L, .) has finite order n, then there are n2 principal loop-isotopes. Some of these n2 loops may be isomorphic, and the main purpose of this paper is to obtain theorems that describe the isomorphism classes. Using these results and a computer, we have determined all the loops of order 6. These are listed (using the Fisher and Yates (2) designations) at the end of the paper.