Centralizing Monoids on a Three-Element Set Related to Binary Idempotent Functions

Abstract

A centralizing monoid M is a set of unary functions which commute with all members of some set F of multi-variable functions. The set F is called a witness of M. In this paper, we study centralizing monoids on a three-element set which have sets of binary idempotent functions as their witnesses. It is shown that the number of such centralizing monoids is 67.