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The relative rank rank(S : A) of a subset A of a semigroup S is the minimum cardinality of a set B such that 〈A ∪ B〉 = S. It follows from a result of Sierpiński that, if X is infinite, the relative rank of a subset of the full transformation semigroup TX is either uncountable or at most 2. A similar result holds for the semigroup BX of binary relations on… (More)
Let a finite semilattice S be a chain under its natural order. We show that if a semigroup T divides a semigroup of full order preserving transformations of a finite chain, then so does any semidirect product S o T .
The relative rank rank(S : U) of a subsemigroup U of a semigroup S is the minimum size of a set V ⊆ S such that U together with V generates the whole of S. As a consequence of a result by Sierpiński it follows that for U ≤ TX , the monoid of all self-maps of an infinite set X, rank(TX : U) is either 0, 1, 2 or uncountable. In this paper we consider the… (More)
Among the most important and intensively studied classes of semigroups are finite semigroups, regular semigroups and inverse semigroups. Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. This connection has lead to a large and deep literature on classifying regular languages by means of… (More)
In this paper we introduce certain order-preserving partial mappings associated with the letters of a primitive word and examine the semigroup thereby generated. The partial mappings act on an ordered chain of length n, the length of the word, in such a way that the action of the word (and each of its conjugates) generates a transitive cycle on the… (More)
This paper describes a method of teaching communication skills to pre-clinical medical students in the setting of general practice. By focusing on the nature of the patient's problem this teaching tries to place interviewing and diagnostic procedures in their proper context in the doctor-patient relationship.