Isoperimetric inequalities for soluble groups
JRJ Groves, SM Hermiller
GEOMETRIAE DEDICATA | KLUWER ACADEMIC PUBL | Published : 2001
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.