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The minimal degree of a finite inverse semigroup


Author: Boris M. Schein
Journal: Trans. Amer. Math. Soc. 333 (1992), 877-888
MSC: Primary 20M30; Secondary 20M18, 20M20
DOI: https://doi.org/10.1090/S0002-9947-1992-1072101-9
MathSciNet review: 1072101
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Abstract: The minimal degree of an inverse semigroup $ S$ is the minimal cardinality of a set $ A$ such that $ S$ is isomorphic to an inverse semigroup of one-to-one partial transformations of $ A$. The main result is a formula that expresses the minimal degree of a finite inverse semigroup $ S$ in terms of certain subgroups and the ordered structure of $ S$. In fact, a representation of $ S$ by one-to-one partial transformations of the smallest possible set $ A$ is explicitly constructed in the proof of the formula. All known and some new results on the minimal degree follow as easy corollaries.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1072101-9
Article copyright: © Copyright 1992 American Mathematical Society

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