Cyclic subsemigroups of symmetric inverse semigroups |
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Authors: | Stephen Leon Lipscomb |
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Institution: | (1) Mary Washington College, 22401 Fredericksburg, Virginia |
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Abstract: | A generalization of the cycle notation for permutations is introduced for partial one-one transformations (charts). Notational
representation theorems for charts that generalize those of permutations are given. Notational multiplication of charts is
developed and then applied to yield a transparent proof of Frobenius' result which bounds the idempotent in the cyclic subsemigroup.
Lastly, the well known result that the structure of the cyclic subgroups of the finite symmetric groups is determined from
combinations of disjoint cycles is generalized to the cyclic subsemigroups of the finite symmetric inverse semigroups. |
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Keywords: | |
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