Geodesic
The order of normalform hypersubstitutions of type (2)
Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 183-192

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In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].
Keywords: hypersubstitutions, terms, idempotent elements, elements of infinite order 
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Denecke, Klaus; Mahdavi, Kazem. The order of normalform hypersubstitutions of type (2). Discussiones Mathematicae. General Algebra and Applications, Tome 20 (2000) no. 2, pp. 183-192. http://geodesic.mathdoc.fr/item/DMGAA_2000_20_2_a2/