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Completely dissociative groupoids

Milton Braitt, David Hobby, Donald Silberger (2012)

Mathematica Bohemica

In a groupoid, consider arbitrarily parenthesized expressions on the k variables x 0 , x 1 , x k - 1 where each x i appears once and all variables appear in order of their indices. We call these expressions k -ary formal products, and denote the set containing all of them by F σ ( k ) . If u , v F σ ( k ) are distinct, the statement that u and v are equal for all values of x 0 , x 1 , x k - 1 is a generalized associative law. Among other results, we show that many small groupoids are completely dissociative, meaning that no generalized associative law holds...

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