2023/08/30 by Ari Markowitz, Markowitz, Ari
Chemistry · #05C05 (Secondary) #20E05 (Primary) 20F65 #20E08 #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2308.16359
openalex publication_date 2023/08/30 · openalex created_date 2023/09/03 · openalex updated_date 2026/07/28
We present an algorithm which takes as input a finite set X of automorphisms of a simplicial tree, and outputs a generating set X' of ⟨ X ⟩ such that either ⟨ X ⟩ is purely hyperbolic and X' is a free basis of ⟨ X ⟩, or X' contains a non-trivial elliptic element. As a special case, the algorithm decides whether a finitely generated group acting on a locally finite tree is discrete and free. This algorithm, which is based on Nielsen's reduction method, works by repeatedly applying Nielsen transformations to X to minimise the generators of X' with respect to a given pre-well-ordering. We use this algorithm to solve the constructive membership problem for finitely generated purely hyperbolic automorphism groups of trees. We provide a Magma implementation of these algorithms, and report its performance.