The Order of Hypersubstitutions of Type τ = (3).

Hypersubstitutions were introduced in [3] as a way of making precise the concepts of hyperidentity and M-hyperidentity. The monoid of hypersubstitutions has been widely studied by many authors. Knowledge of the monoid of hypersubstitutions can be applied to the concept of M-hyperidentities. In this paper, we show that the order of hypersubstitutions of type τ = (3) is 1, 2, 3 or infinite. [ABSTRACT FROM AUTHOR]