Title: Separating automatic from Cayley automatic groups
Abstract: We investigate the problem of distinguishing non-automatic Cayley automatic groups from automatic groups. It is well known that automatic groups are finitely presented with either linear or quadratic Dehn function. In this work we show that any Cayley automatic group with Dehn function that is not almost quadratic, or is not finitely presented, is quantitatively separated from the class of automatic groups via a distance function previously introduced by the first author and Trakuldit.
For each such group we construct a concrete unbounded function, depending only on the group, so that the distance function for any Cayley automatic structure on the group is bounded below by this function.
Publication Year: 2020
Publication Date: 2020-08-05
Language: en
Type: preprint
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Cited By Count: 2
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