Abstract
The setK(G) of all cosets X of a group G, modulo all subgroups of G, forms an inverse semigroup under the multiplication X*Y=smallest coset that constains XY. In this note we show that each inverse semigroup S can be embedded in some coset semigroupK(G). This follows from a result which shows that symmetric inverse semigroups can be embedded in the coset semigroups of suitable symmetric groups. We also give necessary and sufficient conditions on an inverse semigroup S in order that it should be isomorphic to someK(G).
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This research was supported by a grant from the National Science Foundation.
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McAlister, D.B. Embedding inverse semigroups in coset semigroups. Semigroup Forum 20, 255–267 (1980). https://doi.org/10.1007/BF02572685
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DOI: https://doi.org/10.1007/BF02572685