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
@article{10_4153_CMB_1966_049_0,
author = {Jr., E.J. Tully},
title = {On {Semigroups} of {Transformations} {Acting} {Transitively} on a {Set}},
journal = {Canadian mathematical bulletin},
pages = {417--420},
year = {1966},
volume = {9},
number = {4},
doi = {10.4153/CMB-1966-049-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-049-0/}
}
TY - JOUR AU - Jr., E.J. Tully TI - On Semigroups of Transformations Acting Transitively on a Set JO - Canadian mathematical bulletin PY - 1966 SP - 417 EP - 420 VL - 9 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-049-0/ DO - 10.4153/CMB-1966-049-0 ID - 10_4153_CMB_1966_049_0 ER -
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