Geodesic
On Semigroups of Transformations Acting Transitively on a Set
Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 417-420

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We call a semigroup S transitive if S is isomorphic to a semigroup T of transformations of some set M into itself, where T acts on M transitively, that is in such a manner that for all x, y ∊ M we have Xπ = y for some transformation π∊T. In [4] the author showed that S is transitive if and only if there exists a right congruence σ (i.e., an equivalence relation for which a σ b always implies ac σ bc for all c ∊ S) on S, satisfying: (1)There exists a left identity modulo σ, that is an element e such that ea σ a for all a ∊ S . (2)Each σ-class meets each right ideal, or, equivalently, for all a, b ∊ S we have ac σ b for some c ∊ S . (3)The relation σ contains ( i. e. , is less fine than) no left congruence except the identity relation (in which each class consists of a single element). 
Jr., E.J. Tully. On Semigroups of Transformations Acting Transitively on a Set. Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 417-420. doi: 10.4153/CMB-1966-049-0
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[1] 1. Dubreil, P., Contribution à la théorie des demi-groupes. Mem. Acad. Sci. Inst. France (2) 63, no. 3, 52 pages, (1941). Google Scholar

[2] 2. Teissier, M., Sur les équivalences régulières dans les demi-groupes. C.R. Acad. Sci. Paris 232, (1951), pages 1987-1989. Google Scholar

[3] 3. Tully, E.J. Jr., Representation of a semigroup by transformations of a set. Dissertation, Tulane University, (1960), Google Scholar

[4] 4. Tully, E.J. Jr., Representation of a semigroup by transformations acting transitively on a set. Amer. J. Math. 83, (1961), pages 533-541. Errata, Amer. J. Math, 84, (1962), page 386. Google Scholar

[5] 5. Tully, E.J. Jr., Congruence relations on a set with semigroup of transformations. Unpublished. Google Scholar

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