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arXiv · 1112.1634

Homotopy bases and finite derivation type for Schutzenberger groups of monoids

Robert Gray·António Malheiro·Stephen J. Pride
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Abstract

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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Robert Gray, António Malheiro, Stephen J. Pride. 2011-12-07. Homotopy bases and finite derivation type for Schutzenberger groups of monoids. https://doi.org/10.1016/j.jsc.2012.05.006

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