Closed Function Sets on Groups of Prime Order
We give a full description of all sets of functions on the group (ℤp,+) of prime order which are closed under the composition with the clone generated by + from both sides. Thereby, we also get a description of all iterative algebras on ℤp which are closed under the composition with the clone generated by + from both sides. As another consequence, there are infinitely many non finitely generated clones above Clo(ℤp × ℤp,+) for p > 2.
Keywords: Clonoid, iterative algebra, clone, clone classification
2010 Mathematics Subject Classification: 08A40, 08A02