The minimal degree of a finite inverse semigroup

Boris M. Schein
1992 Transactions of the American Mathematical Society  
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
more » ... e formula. All known and some new results on the minimal degree follow as easy corollaries.
doi:10.1090/s0002-9947-1992-1072101-9 fatcat:nalexma7rrcutj6krajux5mpnu