Publication at Faculty of Mathematics and Physics |
2019
Abstract
An equivalence similar to upon a loop is said to be multiplicative if it satisfies x similar to y, u similar to v double right arrow xu similar to yv. Let X be a set with elements x not equal y and let similar to be the least multiplicative equivalence upon a free loop F(X) for which x similar to y.
If a,b is an element of F(X) are such that a not equal b and a similar to b, then neither a\c similar to b\c nor c/a similar to c/b is true, for every c is an element of F(X).