The alternating semigroups: Generators and congruences (Q1184173)

Let \(C_ n\) be the symmetric inverse semigroup of one-one partial transformations of \(n\) symbols. The elements of \(C_ n\) will be called charts. A transpositional is a chart that is either a transposition \((i,j)\) or a semitransposition \((i,j]\) (where \(i\) is mapped to \(j\)). A chart is even if it is a product of an even number of transpositionals. The alternating semigroup \(A^ c_ n\) is the subsemigroup of \(C_ n\) containing the even charts. Generators of \(A^ c_ n\) are identified. For \(n\geq 5\), \(A^ c_ n\) is the collection of restrictions of the even permutations of rank \(n\). It is proved that the congruences of \(A^ c_ n\) form a chain.