Meet-reducible submaximal clones determined by two central relations

Abstract

Let [Formula: see text] and [Formula: see text] be two central relations on a finite set [Formula: see text]. It is known from Rosenberg’s classification theorem (1965) that the clones [Formula: see text] and [Formula: see text] which consist of all operations on [Formula: see text] that preserve [Formula: see text], respectively, [Formula: see text] are among the maximal clones on [Formula: see text]. In this paper, we find all central relations [Formula: see text] such that the clone [Formula: see text] is a maximal subclone of [Formula: see text], where [Formula: see text] is a fixed central relation.