International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 263541, 8 pages
doi:10.1155/2008/263541

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 hypersubstitutions of type τ=(2). In this paper, we use similar methods to characterize idempotent generalized hypersubstitutions of type τ=(2) and determine the order of each generalized hypersubstitution of this type. The main result is that the order is 1,2 or infinite.