Homotopy bases and finite derivation type for Schützenberger groups of monoids

Given a finitely presented monoid and a homotopy base for the monoid, and given an arbitrary Schützenberger group of the monoid, the main result of this paper gives a homotopy base, and presentation, for the Schützenberger group. In the case that the R-class R of the Schützenberger group G (H) has only finitely many H -classes, and there is an element s of the multiplicative right pointwise stabilizer of H, such that under the left action of the monoid on its R-classes the intersection of the orbit of the R-class of s with the inverse orbit of R is finite, then finiteness of the presentation and of the homotopy base is preserved. 2010 Mathematics Subject Classification: 20M50; 20M05, 68Q42