"Polynomial clones on squarefree groups"
, in International Journal of Algebra and Computation, Vol. 18, Nummer 4, Seite(n) 759 - 777, 6-2008, ISSN: 0218-1967
Polynomial clones on squarefree groups
Sprache des Titels:
We prove that, on a set of size n, the number of clones that contain a group operation
and all constant functions is finite if n is squarefree. This confirms a conjecture by Pawe l
Idziak from  where the converse implication was shown. Our result follows from the
observation that the polynomial clone of an expansion of a squarefree group is uniquely
determined by its binary functions. We also note that, in general, such a clone is not
determined by the congruence lattice and the commutator operation of the corresponding
algebra. This refutes a second conjecture from .