2,707 research outputs found
\cPA-isomorphisms of inverse semigroups
A partial automorphism of a semigroup is any isomorphism between its
subsemigroups, and the set all partial automorphisms of with respect to
composition is the inverse monoid called the partial automorphism monoid of
. Two semigroups are said to be \cPA-isomorphic if their partial
automorphism monoids are isomorphic. A class \K of semigroups is called
\cPA-closed if it contains every semigroup \cPA-isomorphic to some
semigroup from \K. Although the class of all inverse semigroups is not
\cPA-closed, we prove that the class of inverse semigroups, in which no
maximal isolated subgroup is a direct product of an involution-free periodic
group and the two-element cyclic group, is \cPA-closed. It follows that the
class of all combinatorial inverse semigroups (those with no nontrivial
subgroups) is \cPA-closed. A semigroup is called \cPA-determined if it is
isomorphic or anti-isomorphic to any semigroup that is \cPA-isomorphic to it.
We show that combinatorial inverse semigroups which are either shortly
connected [5] or quasi-archimedean [10] are \cPA-determined
Automorphisms of partial endomorphism semigroups
In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m 2 N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups:the full transformation semigroup, the partial transformation semigroup, and the symmetric inverse semigroup, and their wreath products, partial endomorphisms of partially ordered sets, the full spectrum of semigroups of partial mappings preserving or reversing a linear or circular order. We also determine the automorphism groups of the so-called Madhaven semigroups as an application of the methods developed herein
Automorphisms of partial endomorphism semigroups
Publicationes Mathematicae DebrecenIn this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures
with a single m-ary relation for any m 2 N over a finite set.
We use this recipe to determine the automorphism groups of the following semigroups:the full transformation semigroup, the partial transformation semigroup, and the symmetric inverse semigroup, and their wreath products, partial endomorphisms of partially ordered sets, the full spectrum of semigroups of partial mappings preserving or reversing a linear or circular order. We also determine the automorphism groups of the so-called Madhaven semigroups as an application of the methods developed herein
Partial Automorphism Semigroups
We study the relationship between algebraic structures and their inverse semigroups of partial automorphisms. We consider a variety of classes of natural structures including equivalence structures, orderings, Boolean algebras, and relatively complemented distributive lattices. For certain subsemigroups of these inverse semigroups, isomorphism (elementary equivalence) of the subsemigroups yields isomorphism (elementary equivalence) of the underlying structures. We also prove that for some classes of computable structures, we can reconstruct a computable structure, up to computable isomorphism, from the isomorphism type of its inverse semigroup of computable partial automorphisms
Inverse monoids of partial graph automorphisms
A partial automorphism of a finite graph is an isomorphism between its vertex
induced subgraphs. The set of all partial automorphisms of a given finite graph
forms an inverse monoid under composition (of partial maps). We describe the
algebraic structure of such inverse monoids by the means of the standard tools
of inverse semigroup theory, namely Green's relations and some properties of
the natural partial order, and give a characterization of inverse monoids which
arise as inverse monoids of partial graph automorphisms. We extend our results
to digraphs and edge-colored digraphs as well
Inverse semigroups with idempotent-fixing automorphisms
A celebrated result of J. Thompson says that if a finite group has a
fixed-point-free automorphism of prime order, then is nilpotent. The main
purpose of this note is to extend this result to finite inverse semigroups. An
earlier related result of B. H. Neumann says that a uniquely 2-divisible group
with a fixed-point-free automorphism of order 2 is abelian. We similarly extend
this result to uniquely 2-divisible inverse semigroups.Comment: 7 pages in ijmart styl
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