  In a paper published in 2012, the second author extended the well-known fact
that Boolean algebras can be defined using only implication and a constant, to
De Morgan algebras-this result led him to introduce, and investigate (in the
same paper), the variety I of algebras, there called implication zroupoids
(I-zroupoids) and here called implicator gruopids (I- groupoids), that
generalize De Morgan algebras. The present paper is a continuation of the paper
mentioned above and is devoted to investigating the structure of the lattice of
subvarieties of I, and also to making further contributions to the theory of
implicator groupoids. Several new subvarieties of I are introduced and their
relationship with each other, and with the subvarieties of I which were already
investigated in the paper mentioned above, are explored.
