Isotopy of Loops
Let and be loops and let be an isotopy. Then it is the product of the principal isotopy from and and the isomorphism between and . Indeed, put, and define the operation * by .
Let and be loops and let e be the neutral element of . Let a principal isotopy from to . Then and where and .
A loop L is a G-loop if it is isomorphic to all its loop isotopes.
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