Geodesic
Inverse semigroups with certain types of partial automorphism monoids
Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 189-195

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Goberstein, Simon M. Inverse semigroups with certain types of partial automorphism monoids. Glasgow mathematical journal, Tome 32 (1990) no. 2, pp. 189-195. doi: 10.1017/S0017089500009204
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