Abstract
The minimal degree of an inverse semigroup S S is the minimal cardinality of a set A A such that S S is isomorphic to an inverse semigroup of one-to-one partial transformations of A A . The main result is a formula that expresses the minimal degree of a finite inverse semigroup S S in terms of certain subgroups and the ordered structure of S S . In fact, a representation of S S by one-to-one partial transformations of the smallest possible set A 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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