Malyshev, Anton; Pak, Igor Growth in product replacement graphs of Grigorchuk groups. (English) Zbl 1366.20029 J. Group Theory 18, No. 2, 209-234 (2015). Summary: The product replacement graph \(\Gamma_{k}(G)\) is the graph on the generating \(k\)-tuples of a group \(G\), with edges corresponding to Nielsen moves. We prove the exponential growth of product replacement graphs \(\Gamma_{k}(\mathbb G_\omega)\) of Grigorchuk groups, for \(k \geq 5\). MSC: 20F69 Asymptotic properties of groups 20F65 Geometric group theory 20E08 Groups acting on trees 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) Keywords:product replacement graph; Nielsen moves; exponential growth; Grigorchuk groups PDFBibTeX XMLCite \textit{A. Malyshev} and \textit{I. Pak}, J. Group Theory 18, No. 2, 209--234 (2015; Zbl 1366.20029) Full Text: DOI arXiv