J. Aust. Math. Soc.
81 (2006), 185198

Inverse semigroups determined by their partial automorphism monoids

Simon M. Goberstein
Department of Mathematics and Statistics
California State University
Chico, CA 95929
USA
SGoberstein@csuchico.edu



Abstract

The partial automorphism monoid of an inverse
semigroup is an inverse monoid consisting of all
isomorphisms between its inverse subsemigroups.
We prove that a tightly connected fundamental
inverse semigroup
with no isolated nontrivial subgroups is lattice
determined `modulo semilattices' and if
is an inverse semigroup whose partial
automorphism monoid is isomorphic to that of
, then either
and
are isomorphic or they are dually isomorphic
chains relative to the natural partial order; a
similar result holds if
is any semigroup and the inverse monoids
consisting of all isomorphisms between
subsemigroups of
and
, respectively, are isomorphic. Moreover, for
these results to hold, the conditions that
be tightly connected and have no isolated
nontrivial subgroups are essential.

Download the article in PDF format (size 121 Kb)


Australian Mathematical Publishing Association Inc.

©
Australian MS

