2012/09/18 by Michelle Bucher, Bucher, Michelle, Alexey Talambutsa +1
Mathematics · #20E06 #20E08 #20F65 #20F69 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20E06 #msc:20E08 #msc:20F65 #msc:20F69
paper · pdf · doi:10.48550/arxiv.1209.4071
17 pages, 7 figures
arxiv created 2012/09/18 · openalex publication_date 2012/09/18 · arxiv updated 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We prove that there is a gap between √(2) and (1+√(5))/2 for the exponential growth rate of free products G=A*B not isomorphic to the infinite dihedral group. For amalgamated products G=A*C B with ([A:C]-1)([B:C]-1)≥2, we show that lower exponential growth rate than √(2) can be achieved by proving that the exponential growth rate of the amalgamated product PGL(2,ℤ)≅ (C2× C2) *C2 D6 is equal to the unique positive root of the polynomial z3-z-1. This answers two questions by Avinoam Mann [The growth of free products, Journal of Algebra 326, no. 1 (2011) 208--217].