Maximal subsemilattices of the full transformation semigroup
\textit{B. M. Schein} has posed the problem of determining the maximal subsemilattices of the full transformation semigroup T(X) on a finite set X. He has shown [Algebraic theory of semigroups, Szeged/Hung. 1976, Colloq. Math. Soc. János Bolyai 20, 519-544 (1979; Zbl 0405.08006)] that every subsemilattice S of T(X) induces, in a natural way, a partial order on X (called the transitivity order and denoted by TR(S)) which satisfies a number of conditions. Moreover S is completely determined by TR(S) together with the fixed point sets of S. The present authors look at the problem of determining precisely which of those partial orders on X determine maximal subsemilattices and they characterize these subsemilattices in the main results. This paper is a research announcement and consequently, contains no proofs. A paper with the same title, complete with proofs, has been submitted for publication.
scientific article; zbMATH DE number 3991789