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Inverse semigroups with certain types of partial automorphism monoids

Published online by Cambridge University Press:  18 May 2009

Simon M. Goberstein
Simon M. Goberstein
Affiliation:
Department of Mathematics and Statistics, California State University, Chico Chico, California 95929-0525
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Abstract

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For an inverse semigroup S, the set of all isomorphisms betweeninverse subsemigroups of S is an inverse monoid under composition which is denoted by (S) and called the partial automorphism monoid of S. Kirkwood [7] and Libih [8] determined which groups have Clifford partial automorphism monoids. Here we investigate the structure of inverse semigroups whose partial automorphism monoids belong to certain other important classes of inverse semigroups. First of all, we describe (modulo so called “exceptional” groups) all inverse semigroups S such that (S) is completely semisimple. Secondly, for an inverse semigroup S, we find a convenient description of the greatest idempotent-separating congruence on (S), using a well-known general expression for this congruence due to Howie, and describe all those inverse semigroups whose partial automorphism monoids are fundamental.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 2 , May 1990 , pp. 189 - 195
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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