The alternating semigroups: Generators and congruences

The idea of an even permutation has recently been generalized, via path notation, to one-one partial transformations (charts) in the symmetric inverse semigroupsC _n. The even charts form the alternating semigroupA _n ^c ⊂C _n . Generators ofA _n ^c are identified: It then follows that forn≥5,A _n ^c is the collection of restrictions of the even permutations (of rankn). Like theC _n case, the congruences ofA _n ^c form a chain. Part of this research was supported by a Mary Washington College faculty development grant.