scholarly journals Maximal subgroups of free idempotent-generated semigroups over the full transformation monoid

2012 ◽  
Vol 104 (5) ◽  
pp. 997-1018 ◽  
Author(s):  
R. Gray ◽  
N. Ruškuc
Keyword(s):  
Maximal Subgroups ◽  
Full Transformation ◽  
Transformation Monoid

scholarly journals An extension of properties of symmetric group to monoids and a pretorsion theory in a category of mappings

2019 ◽  
Vol 18 (12) ◽  
pp. 1950234 ◽  
Author(s):  
Alberto Facchini ◽  
Leila Heidari Zadeh
Keyword(s):  
Symmetric Group ◽  
Full Transformation ◽  
Transformation Monoid ◽  
Finite Set ◽  
Torsion Part

Several elementary properties of the symmetric group [Formula: see text] extend in a nice way to the full transformation monoid [Formula: see text] of all maps of the set [Formula: see text] into itself. The group [Formula: see text] turns out to be the torsion part of the monoid [Formula: see text]. That is, there is a pretorsion theory in the category of all maps [Formula: see text], [Formula: see text] an arbitrary finite set, in which bijections are exactly the torsion objects.

scholarly journals Centralising Monoids with Low-Arity Witnesses on a Four-Element Set

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1471
Author(s):  
Mike Behrisch ◽  
Edith Vargas-García
Keyword(s):  
The Other ◽  
Full Transformation ◽  
Group Operation ◽  
Binary Operations ◽  
Other Hand ◽  
Transformation Monoid ◽  
Element Set

As part of a project to identify all maximal centralising monoids on a four-element set, we determine all centralising monoids witnessed by unary or by idempotent binary operations on a four-element set. Moreover, we show that every centralising monoid on a set with at least four elements witnessed by the Maľcev operation of a Boolean group operation is always a maximal centralising monoid, i.e., a co-atom below the full transformation monoid. On the other hand, we also prove that centralising monoids witnessed by certain types of permutations or retractive operations can never be maximal.

scholarly journals HALL'S CONDITION AND IDEMPOTENT RANK OF IDEALS OF ENDOMORPHISM MONOIDS

2008 ◽  
Vol 51 (1) ◽  
pp. 57-72 ◽  
Author(s):  
R. Gray
Keyword(s):  
Simple Semigroup ◽  
Analogous Result ◽  
Direct Consequence ◽  
Full Transformation ◽  
Generating Set ◽  
Endomorphism Monoids ◽  
Idempotent Rank ◽  
Transformation Monoid ◽  
Hall's Condition ◽  
Property Holding

AbstractIn 1990, Howie and McFadden showed that every proper two-sided ideal of the full transformation monoid $T_n$, the set of all maps from an $n$-set to itself under composition, has a generating set, consisting of idempotents, that is no larger than any other generating set. This fact is a direct consequence of the same property holding in an associated finite $0$-simple semigroup. We show a correspondence between finite $0$-simple semigroups that have this property and bipartite graphs that satisfy a condition that is similar to, but slightly stronger than, Hall's condition. The results are applied in order to recover the above result for the full transformation monoid and to prove the analogous result for the proper two-sided ideals of the monoid of endomorphisms of a finite vector space.

scholarly journals On the Monoid of Unital Endomorphisms of a Boolean Ring

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 305
Author(s):  
Bana Al Al Subaiei ◽  
Noômen Jarboui
Keyword(s):  
Automorphism Group ◽  
Explicit Description ◽  
Boolean Ring ◽  
Full Transformation ◽  
Unital Ring ◽  
Transformation Monoid ◽  
Power Set

Let X be a nonempty set and P(X) the power set of X. The aim of this paper is to provide an explicit description of the monoid End1P(X)(P(X)) of unital ring endomorphisms of the Boolean ring P(X) and the automorphism group Aut(P(X)) when X is finite. Among other facts, it is shown that if X has cardinality n≥1, then End1P(X)(P(X))≅Tnop, where Tn is the full transformation monoid on the set X and Aut(P(X))≅Sn.

scholarly journals Largest subsemigroups of the full transformation monoid

2008 ◽  
Vol 308 (20) ◽  
pp. 4801-4810 ◽  
Author(s):  
R. Gray ◽  
J.D. Mitchell
Keyword(s):  
Full Transformation ◽  
Transformation Monoid
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