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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom