Schützenberger group

In semigroup theory, a Schützenberger group is a group associated with a Green H-class of a semigroup. The Schützenberger groups associated with different H-classes are distinct, but the groups associated with two different H-classes contained in the same D-class of a semigroup are isomorphic. Moreover, if the H-class itself were a group, the Schützenberger group of the H-class would be isomorphic to the H-class. In fact, there are two Schützenberger groups associated with a given H-class, with each being antiisomorphic to the other.

The Schützenberger group was discovered by Marcel-Paul Schützenberger in 1957 and the terminology was coined by A. H. Clifford.