A classification of maximal idempotent-generated subsemigroups of finite orientation-preserving singular partial transformation semigroups

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 PO^k_n\mathit{PO}^{k}_{n} with respect to ≤ _k .     

Graphs and finite transformation semigroups

Given a finite set X and a semigroup S of transformations of X, we study the orbitoids of S on X and on X² and, assuming S transitive, those of the statbilizer in S of an element α ∈ X. The action of S as a semigroup of endomorphisms of some relevant graphs (having X as vertex set) is also considered.     

Endomorphisms of finite full transformation semigroups

We describe all endomorphisms of finite full transformation semigroups and count their number.

     

奇异保序变换半群的极大正则子半群

设On为通常的有限链Xn={1,2,…,n}上的奇异保序变换半群.文中利用格林关系的方法讨论On的极大正则子半群,确定了On的所有的极大正则子半群.     

Locally maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups

In this paper we study locally maximal idempotent-generated subsemigroups of finite singular orientation-preserving transformation semigroups. This work is supported by N.S.F. and E.S.F. of Guizhou.     

Some remarks on finite full transformation semigroups

Communicated by J. M. Howie     

Products of idempotents in finite full transformation semigroups

Communicated by J. M. Howie     

A classification of the maximal idempotent-generated subsemigroups of finite singular semigroups

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     

A classification of maximal idempotent-generated subsemigroups of singular orientation-preserving transformation semigroups

We describe maximal idempotent-generated subsemigroups of finite singular orientation-preserving transformation semigroups and completely obtain their classification. This work is supported by N.S.F. and E.S.F. of Guizhou.     

Decidability of finite quasivarieties generated by certain transformation semigroups

No Abstract. Received January 2, 2000; accepted in final form August 28, 2000.     

A classification of maximal subsemigroups of finite order-preserving transformation semigroups

We describe the maximal subsemigroups of the semigroup of all order-preserving transformations of a finite chain and completely obtain their classification. We also count the number of its maximal subsemigroups.     

Maximal properties of some subsemigroups in finite order-preserving transformation semigroups

Let [n] = {1,2,…,n} be a finite set, ordered in the usual way. The order-preserving transformation semigroup O_n 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 O_n has 2n - 2 such subsemi-groups. Secondly, we investigate maximal regular subsemigroups of O_n , and obtain the number of such subsemigroups as 2n - 3. Thirdly, we describe maximal idempotent-generated regular subsemigroups of O_n , and also obtain their classification and number.     

Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances

Let Ω^Ω be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of Ω^Ω, then we write U≈V if there exists a finite subset F of Ω^Ω such that the subsemigroup generated by U and F equals that generated by V and F. The relative rank of U in Ω^Ω is the least cardinality of a subset A of Ω^Ω such that the union of U and A generates Ω^Ω. In this paper we study the notions of relative rank and the equivalence ≈ for semigroups of endomorphisms of binary relations on Ω.The semigroups of endomorphisms of preorders, bipartite graphs, and tolerances on Ω are shown to lie in two equivalence classes under ≈. Moreover such semigroups have relative rank 0, 1, 2, or d in Ω^Ω where d is the minimum cardinality of a dominating family for N^N. We give examples of preorders, bipartite graphs, and tolerances on Ω where the relative ranks of their endomorphism semigroups in Ω^Ω are 0, 1, 2, and d.We show that the endomorphism semigroups of graphs, in general, fall into at least four classes under ≈ and that there exist graphs where the relative rank of the endomorphism semigroup is 2^ℵ₀.     

Defining relations for idempotent generators in finite partial transformation semigroups

We give a presentation for the semigroup of all singular partial transformations on a finite set, in terms of the generating set consisting of all idempotent partial transformations of corank 1.     

Defining relations for idempotent generators in finite full transformation semigroups

In 1966, John Howie showed that the semigroup $\mathcal{T}_{n}\setminus \mathcal{S}_{n}$ of all singular transformations on a n element set is generated by the set of all idempotent transformations of rank n?1. We give a presentation for $\mathcal{T}_{n}\setminus \mathcal{S}_{n}$ in terms of this generating set.     

Generating sets of elements of Chevalley groups over a finite field

Translated from Algebra i Logika, Vol. 28, No. 6, pp. 670–686, November–December, 1989.