Embedding inverse semigroups in coset semigroups |
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Authors: | D B McAlister |
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Institution: | (1) Department of Mathematical Sciences, Northern Illinois University, 60115 DeKalb, IL |
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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).
This research was supported by a grant from the National Science Foundation. |
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Keywords: | |
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