The order of generalized hypersubstitutions of type \(\tau =(2)\) (Q1008547)

Summary: The order of hypersubstitutions, all idempotent elements on the monoid of all hypersubstitutions of type \(\tau =(2)\) were studied by K. Denecke and Sh. L. Wismath and all idempotent elements on the monoid of all hypersubstitutions of type \(\tau =(2,2)\) were studied by Th. Changpas and K. Denecke. We want to study similar problems for the monoid of all generalized hypersubstitutions of type \(\tau =(2)\). In this paper, we use similar methods to characterize idempotent generalized hypersubstitutions of type \(\tau =(2)\) and determine the order of each generalized hypersubstitution of this type. The main result is that the order is 1, 2 or infinite.