Paper Info
Title
Lower Bounds On The Growth Of A Group Acting On The Binary Rooted Tree
Abstract
AMS Mathematics Subject Classification: 20F32 (Geometric group theory), 16P90 (Growth rate), 20E08 (Groups acting on trees), 05C25 (Graphs and groups)In 1980, Rostislav Grigorchuk constructed an infinite finitely generated torsion 2-group G, called the first Grigorchuk group, and in 1983 showed that it is of intermediate growth, with the following estimates on its growth function gamma (See [6]):e(rootn) less than or similar to gamma (n) less than or similar to e(n beta),where beta = log(32)(31) approximate to 0.991. He conjectured that the lower bound is actually tight.In this paper we improve the lower bound toe(n alpha) less than or similar to gamma (n),where alpha approximate to 0.5157, and thus disproves the conjecture.
Year
DOI
Venue
2001
10.1142/S0218196701000395
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
Keywords
Field
DocType
lower bound
Grigorchuk group,Growth function,Discrete mathematics,Combinatorics,Finitely-generated abelian group,Algebra,Torsion (mechanics),Upper and lower bounds,Conjecture,Mathematics,Binary number
Journal
Volume
Issue
ISSN
11
1
0218-1967
Citations 
PageRank 
References 
2
0.64
0
Authors
1
Name
Order
Citations
PageRank
Laurent Bartholdi1278.74