The order of normal form hypersubstitutions of type (2) (Q2717942)

Hypersubstitutions were orginally introduced to facilitate the study of hyperidentities of varieties, but they have proved to be of interest in their own right. In particular, there is the question of their order. In a previous paper [\textit{K. Denecke, D. Lau, R. Pöschel} and \textit{D. Schweigert}, Contrib. Gen. Algebra 7, 97-118 (1991; Zbl 0759.08005)] it was shown that all hypersubstitutions of type (2) which are neither idempotent, nor the substitution which interchanges the variables have infinite order. The purpose of this paper is to study hypersubstitutions within certain varieties of semigroups and it is shown that there are other hypersubstitutions of finite order in such situations.