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1.
We study the structure of the semigroup OT n , which is a unique (up to an isomorphism) R-section of the semigroup T n . For this semigroup, we describe Green relations, determine regular and nilpotent elements, describe maximal nilpotent subsemigroups, and determine the unique irreducible system of generatrices and maximal subsemigroups.  相似文献   

2.
Let [n] = {1,2,…,n} be a finite set, ordered in the usual way. The order-preserving transformation semigroup On is the set of all order-preserving transformations of [n] (excluding the identity mapping) under composition. In this paper we first describe maximal idempotent-generated subsemigroups of O n, and show that On has 2n - 2 such subsemi-groups. Secondly, we investigate maximal regular subsemigroups of On , and obtain the number of such subsemigroups as 2n - 3. Thirdly, we describe maximal idempotent-generated regular subsemigroups of On , and also obtain their classification and number.  相似文献   

3.
Abstract. We study the structure of the semigroup IO n of all order-preserving partial bijections on an n -element set. For this semigroup we describe maximal subsemigroups, maximal inverse subsemigroups, automorphisms and maximal nilpotent subsemigroups. We also calculate the maximal cardinality for the nilpotent subsemigroups in IO n which happens to be given by the n -th Catalan number.  相似文献   

4.
Let Tn be the full transformation semigroup on the n-element set Xn. For an arbitrary integer r such that 2 ≤ r ≤ n-1, we completely describe the maximal subsemigroups of the semigroup K(n, r) = {α∈Tn : |im α| ≤ 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 Tn.  相似文献   

5.
For the factor-powerFP(S n ) of the symmetric groupS n , we describe regular elements, maximal subgroups, isolated and fully isolated subsemigroups, and also maximal nilpotent subsemigroups whose zero elements coincide with the zero element of the semigroupFP(S n ). Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 341–354, September, 1995. This research was partially supported by the Foundation for Fundamental Research of the State Committee for Science and Engineering of the Ukraine.  相似文献   

6.
We study the structure of the semigroup IO n of all order-preserving partial bijections on an n-element set. For this semigroup we describe maximal subsemigroups, maximal inverse subsemigroups, automorphisms and maximal nilpotent subsemigroups. We also calculate the maximal cardinality for the nilpotent subsemigroups in IO n which happens to be given by the n-th Catalan number.  相似文献   

7.
We describe the maximal idempotent-generated subsemigroups of the finite singular semigroup Sing n on the finite set X n ={1,2, \ldots,n} , and count the number of its maximal idempotent-generated subsemigroups. October 21, 1999  相似文献   

8.
We study mathematical models of the structure of nilpotent subsemigroups of the semigroup PTD(B n ) of partial contracting transformations of a Boolean, the semigroup TD(B n ) of full contracting transformations of a Boolean, and the inverse semigroup ISD(B n ) of contracting transformations of a Boolean. We propose a convenient graphical representation of the semigroups considered. For each of these semigroups, the uniqueness of its maximal nilpotent subsemigroup is proved. For PTD(B n ) and TD(B n ) , the capacity of a maximal nilpotent subsemigroup is calculated. For ISD(B n ), we construct estimates for the capacity of a maximal nilpotent subsemigroup and calculate this capacity for small n. For all indicated semigroups, we describe the structure of nilelements and maximal nilpotent subsemigroups of nilpotency degree k and determine the number of elements and subsemigroups for some special cases.  相似文献   

9.
In this paper we describe the maximal idempotent-generated subsemigroups of the finite orientation-preserving singular partial transformation semigroup SPOP n and obtain their complete classification. We also obtain a classification of the maximal idempotent-generated subsemigroups of the finite order-preserving singular partial transformation semigroup POkn\mathit{PO}^{k}_{n} with respect to ≤ k .  相似文献   

10.
We describe maximal regular subsemibands of the singular transformation semigroup Singn on the set Xn = {1, 2, . . . n} and obtain their complete classification We show that Singn has n(n + 1)/2 maximal regular subsemibands, and formulate the cardinal number of such subsemigroups.  相似文献   

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