# António Malheiro

## Assistant Professor, Mathematical Department

Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)

Faculdade de Ciências e Tecnologia UNL, Monte da Caparica, 2829-516 Caparica, Tel: (+351) 212948388 ext. 10832 (email)

- Citation:
- Gray, R. D., A. Malheiro, and S. J. Pride. "Homotopy bases and finite derivation type for Schützenberger groups of monoids." J. Symb. Comput.. 50 (2013): 50-78.

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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