Complete semigroups of binary relations determined by three-element \(X\)-chains. (Q1416170)

This paper considers the subgroups of the semigroup of binary relations \(B_X\) consisting of binary relations \(R\) whose sections \(S_x=\{y\mid(x,y)\in R\}\) are always equal to some \(Z_i\), for a 3 element chain \(Z_1\subset Z_2\subset Z_3\). It determines idempotents, regular elements, maximal semigroups consisting of idempotents, and irreducible generating sets, and computes the cardinalities of some of these for finite sets.