Discrete and free groups acting on locally finite trees

2021/10/21 by Conder, Matthew J.
#20E08 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2110.10904

Abstract

We present an algorithm to decide whether or not a finitely generated subgroup of the isometry group of a locally finite simplicial tree is both discrete and free. The correctness of this algorithm relies on the following conjecture: every `minimal' n-tuple of isometries of a simplicial tree either contains an elliptic element or satisfies the hypotheses of the Ping Pong Lemma. We prove this conjecture for n=2,3, and show that it implies a generalisation of Ihara's Theorem.

Related

• Recognition and constructive membership for purely hyperbolic groups acting on trees
• Groups acting faithfully on trees and properly on products of trees
• Discrete (P)-closed Groups Acting On Trees
• Simple groups of automorphisms of trees determined by their actions on finite subtrees
• Simple groups and irreducible lattices in wreath products