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Isoperimetric Inequalities for Soluble Groups |
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| Authors: | J. R. J. Groves S. M. Hermiller |
| Affiliation: | 1. Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC, 3052, Australia 2. Department of Mathematics and Statistics, University of Nebraska Lincoln, Lincoln, NE, 68588, U.S.A. |
| 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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