Journal of Symbolic Computation, volume 50 (2013), 50 - 78

Given a finitely presented monoid and a homotopybase for the monoid, and given an arbitrary Schützenbergergroup of the monoid, the main result of this paper gives a homotopybase, and presentation, for the Schützenbergergroup. In the case that the R-class R of the SchützenbergergroupG(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 homotopybase is preserved.