The gap in the growth of residually soluble groups
John S. Wilson · Bulletin of the London Mathematical Society · 2011
Let G be a group with a finite generating set X and, for each n ∈ ℕ, let γX(n) denote the number of products of n elements of X ∪ X−1 ∪ {1}. It is proved that if G is residually soluble and γ x ( n ) / e ( n 1 / 6 ) → 0 as n → ∞, then G must be virtually nilpotent.