The order of generalized hypersubstitutions of type τ = (2)

Abstract

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