The minimal degree of a finite inverse semigroup
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- by Boris M. Schein PDF
- Trans. Amer. Math. Soc. 333 (1992), 877-888 Request permission
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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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