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Geometric Group Theory Down Under
We show that a central extension of a group H by an abelian group A has an automatic structure with A a rational subgroup if and only if H has an automatic structure for which the extension is given by a \regular" cocycle. This had been proved for biautomatic structures by Neumann and Reeves. We m a k e a start at classifying automatic structures on such groups, but we show that, at least for automatic structures, a classi cation using \controlling subgroups," as done by the authors in certaindoi:10.1515/9783110806861.261 fatcat:ftxmgtwlebbzvbm3symdgqasse