Premium
The gap in the growth of residually soluble groups
Author(s) -
Wilson John S.
Publication year - 2011
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdq124
Subject(s) - mathematics , nilpotent , set (abstract data type) , combinatorics , group (periodic table) , pure mathematics , chemistry , organic chemistry , computer science , programming language
Let G be a group with a finite generating set X and, for each n ∈ ℕ, let γ X ( 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.