J. Aust. Math. Soc.
81 (2006), 185-198|
Inverse semigroups determined by their partial automorphism monoids
Simon M. Goberstein|
Department of Mathematics and Statistics
California State University
Chico, CA 95929
| 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
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
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
, respectively, are isomorphic. Moreover, for
these results to hold, the conditions that
be tightly connected and have no isolated
nontrivial subgroups are essential.
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