# Homotopy bases and finite derivation type for subgroups of monoids - Mathematics > Group Theory

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Abstract: Given a monoid defined by a presentation, and a homotopy base for thederivation graph associated to the presentation, and given an arbitrarysubgroup of the monoid, we give a homotopy base and presentation for thesubgroup. If the monoid has finite derivation type FDT, and if under theaction of the monoid on its subsets by right multiplication the strong orbit ofthe subgroup is finite, then we obtain a finite homotopy base for the subgroup,and hence the subgroup has FDT. As an application we prove that a regularmonoid with finitely many left and right ideals has FDT if and only if all ofits maximal subgroups have FDT. We use this to show that a finitely presentedregular monoid with finitely many left and right ideals satisfies thehomological finiteness condition FP 3 if all of its maximal subgroups satisfythe condition FP 3.

Author: ** Robert Gray, AntÃ³nio Malheiro**

Source: https://arxiv.org/