Yang, Hao Bo et Yang, Xiu Liang, Maximal Subsemigroups of Finite Transformation Semigroups K(n, r), Acta mathematica Sinica. English series (Print) , 20(3), 2004, pp. 475-482
Let T n be the full transformation semigroup on the n-element set X n . For an arbitrary integer r such that 2 r n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = { T n : |im | r}. We also formulate the cardinal number of such subsemigroups which is an answer to Problem 46 of Tetrad in 1969, concerning the number of subsemigroups of T n .