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View article: Conjugacy in Semigroups: the Partition and Brauer Diagram Monoids, Conjugacy Growth, and Partial Inner Automorphisms
Conjugacy in Semigroups: the Partition and Brauer Diagram Monoids, Conjugacy Growth, and Partial Inner Automorphisms Open
The conjugacy relation plays an important role in group theory. If $a$ and $b$ are elements of a group~$G$, $a$ is conjugate to $b$ if $g^{-1}ag=b$ for some $g\in G$. Group conjugacy extends to inverse semigroups in a natural way: for $a$ …
View article: CREAM: a Package to Compute [Auto, Endo, Iso, Mono, Epi]-morphisms, Congruences, Divisors and More for Algebras of Type $(2^n,1^n)$
CREAM: a Package to Compute [Auto, Endo, Iso, Mono, Epi]-morphisms, Congruences, Divisors and More for Algebras of Type $(2^n,1^n)$ Open
The CREAM GAP package computes automorphisms, congruences, endomorphisms and subalgebras of algebras with an arbitrary number of binary and unary operations; it also decides if between two such algebras there exists a monomorphism, an epim…
View article: A transversal property for permutation groups motivated by partial transformations
A transversal property for permutation groups motivated by partial transformations Open
In this paper we introduce the definition of the (k,l)-universal transversal property for permutation groups, which is a refinement of the definition of k-universal transversal property, which in turn is a refinement of the classical defin…
View article: The existential transversal property: A generalization of homogeneity and its impact on semigroups
The existential transversal property: A generalization of homogeneity and its impact on semigroups Open
Let $G$ be a permutation group of degree $n$, and $k$ a positive integer with $k\le n$. We say that $G$ has the $k$-existential property, or $k$-et for short, if there exists a $k$-subset $A$ of the domain $Ω$ such that, for any $k$-partit…
View article: A Transversal Property for Permutation Groups Motivated by Partial\n Transformations
A Transversal Property for Permutation Groups Motivated by Partial\n Transformations Open
In this paper we introduce the definition of $(k,l)$-universal transversal\nproperty, which is a refinement of the definition of $k$-universal transversal\nproperty, which in turn is a refinement of the classic definition of\n$k$-homogenei…
View article: Finite affine algebras are fully dualizable
Finite affine algebras are fully dualizable Open
We show that every finite affine algebra A admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure A∼ of finite type. We give an explicit bound on the …
View article: Orbits of primitive k-homogenous groups on (N − k)-partitions with applications to semigroups
Orbits of primitive k-homogenous groups on (N − k)-partitions with applications to semigroups Open
© 2018 American Mathematical Society. The purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do t…
View article: Congruences on Direct Products of Transformation and Matrix Monoids
Congruences on Direct Products of Transformation and Matrix Monoids Open
Malcev described the congruences of the monoid $T_n$ of all full transformations on a finite set $X_n=\{1, \dots,n\}$. Since then, congruences have been characterized in various other monoids of (partial) transformations on $X_n$, such as …