19 citations · 52 across the 8 of their papers we have counts for
9 papers
The Inverse Monoid of Partial Inner Automorphisms of a Semigroup
João Araújo, Wolfram Bentz, Michael Kinyon +4
We introduce the inverse monoid of inner partial automorphisms of a semigroup -- a tool that associates to every semigroup an inverse semigroup. When the semigroup is a group, this…
Conjugacy in Abstract Semigroups, Transformation and Diagram Monoids, and Conjugacy Growth
João Araújo, Wolfram Bentz, Michael Kinyon +3
We study conjugacy relations on semigroups and monoids, focusing on the relation $a \cfn b$, defined by the existence of such that , , , an…
Conjugacy in inverse semigroups
Joao Araujo, Michael Kinyon, Janusz Konieczny
In a group , elements and are conjugate if there exists such that . This conjugacy relation, which plays an important role in group theory, can be…
Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids
João Araújo, Michael Kinyon, Janusz Konieczny +1
There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems fo…
Four Notions of Conjugacy for Abstract Semigroups
J. Araújo, Michael Kinyon, Janusz Konieczny +1
The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been many attempts to find notions of c…
The Largest Subsemilattices of the Endomorphism Monoid of an Independence Algebra
João Araújo, Wolfram Bentz, Janusz Konieczny
An algebra $\A$ is said to be an independence algebra if it is a matroid algebra and every map $\al:X\to A$, defined on a basis of $\A$, can be extended to an endomorphism of $…
Conjugation in Semigroups
João Araújo, Janusz Konieczny, António Malheiro
The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the not…
The Largest Subsemilattices of the Semigroup of Transformations on a Finite Set
João Araújo, Janusz Konieczny
Let T(X) be the semigroup of full transformations on a finite set X with n elements. We prove that every subsemilattice of T(X) has at most 2^{n-1} elements and that there are prec…
Minimal paths in the commuting graphs of semigroups
Joao Araujo, Michael Kinyon, Janusz Konieczny
Let be a finite non-commutative semigroup. The commuting graph of , denoted $\cg(S)$, is the graph whose vertices are the non-central elements of and whose edges are the…