A note on finite generated subsemigroups of T(X,Y)
Nareupanat Lekkoksung, Jörg Koppitz · Mathematics for Applications · 2015
It is well known that a countable set of transformations on an infinite set X is contained in a two-generated subsemigroup of the full transformation semigroup on X.If Y ⊂ X, then T (X, Y ), the set of all transformations on X with an image in Y , forms a semigroup of transformations with restricted range, as shown in 1975 by Symons [10].In this paper, we give a sufficient and necessary condition for a countable subset of T (X, Y ) to be contained in a three-generated subsemigroup of T (X, Y ).MSC (2010): primary 20M15, 20M20, 20M99.