Homotopy bases and finite derivation type for Schutzenberger groups of monoids

Details Homotopy bases and finite derivation type for Schutzenberger groups of monoids Homotopy bases and finite derivation type for Schutzenberger groups of monoids

2011-12-07

arxiv.org/abs/1112.1634v1

Mathematics

Group Theory

24 pages

Scientific paper

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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