Centralizing Monoids on a Three-Element Set

Let A be a finite set with |A|>; 1. A centralizing monoid on A is a set of unary functions defined on A which commute with some set of (multi-variable) functions on A. In this paper we consider the case where A is a three-element set. Using the concept of a witness and Kuznetsov criterion, we determine all centralizing monoids on a three-element set. There are 192 centralizing monoids, which are divided into 48 conjugate classes.

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