Abstract
We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-Abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic.
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Groves, J.R.J., Hermiller, S.M. Isoperimetric Inequalities for Soluble Groups. Geometriae Dedicata 88, 239–254 (2001). https://doi.org/10.1023/A:1013110821237
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DOI: https://doi.org/10.1023/A:1013110821237