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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Famous quotes containing the word loops:
“An accurate charting of the American woman’s progress through history might look more like a corkscrew tilted slightly to one side, its loops inching closer to the line of freedom with the passage of time—but like a mathematical curve approaching infinity, never touching its goal. . . . Each time, the spiral turns her back just short of the finish line.”
—Susan Faludi (20th century)