Isoperimetric Inequalities for Soluble Groups |
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| Authors: | J R J Groves S M Hermiller |
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| Institution: | 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.
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| 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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