Maximal Centralizing Monoids and their Relation to Minimal Clones

A centralizing monoid is a set of unary functions on a fixed set A which commute with some set of functions on A. It is known to be hard to determine effectively such centralizing monoids. In this paper we focus on maximal centralizing monoids. It is proved that they have strong connection to minimal clones. We determine all maximal centralizing monoids on a three-element set and, then, prove a general result relating constant functions to maximal centralizing monoids.