Orders of Generalized Hypersubstitutions of Type τ =(3)

The concept of generalized hypersubstitutions was introduced by S. Leeratanavalee and K. Denecke in 2000. We used it as the tool to study strong hyperidentities and strongly solid varieties. In this paper we characterize all idempotent generalized hypersubstitutions of type τ =(3) and determine the order of each generalized hypersubstitution of this type. It turns out that the order is 1, 2, 3 or infinite.