Maximal Subsemigroups of Finite Transformation Semigroups K(n, r)

Authors
Yang, Hao Bo Yang, Xiu Liang
Citation
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
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
20
Issue
3
Year of publication
2004
Pages
475 - 482
Database
ACNP
SICI code
Abstract
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 .