%0 Journal Article %J J. Symb. Comput. %D 2013 %T Homotopy bases and finite derivation type for Schützenberger groups of monoids. %A R.D. {Gray} %A Malheiro, A. %A S.J. {Pride} %I Elsevier (Academic Press), London %P 50–78 %R 10.1016/j.jsc.2012.05.006 %U http://dx.doi.org/10.1016/j.jsc.2012.05.006 %V 50 %X

Given a finitely presented monoid and a homotopy base for the monoid, and given an arbitrary Schutzenberger group of the monoid, the main result of this paper gives a homotopy base, and presentation, for the Schutzenberger group. In the case that the R-class R' of the Schutzenberger 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.

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