Search for Some Majority Operation and Studies of its Centralizing Monoid

A centralizing monoid M is a set of unary operations which commute with some set F of operations. Here F is called a witness of M.On a 3-element set, majority minimal operations serve as witnesses of maximal centralizing monoids. In this paper, we start with one such majority operation and obtain its generalization, called mb, on a k-element set for any k ≥ 3. We explicitly describe the centralizing monoid M(mb) with mb as its witness and then prove it is not maximal if k > 3, contrary to the fact for k = 3.