An Explicit Generating Pair for Radu's Simple Tree Lattice

We give an explicit generating pair for the torsion-free infinite simple group in Corollary IV(ii) of Radu's paper on lattices in products of trees. In the notation of that presentation, the pair is x1*x3 and x1*y3. Only the first five displayed equations are needed: a short group calculation expresses every original generator in this pair. In particular, the minimum generator number of this specific group is two. We also give a two-generator presentation with seven defining equations. This excludes one concrete candidate for a finitely presented simple group that is not two-generated; it does not resolve the general existence question. This is an unrefereed preprint. No absolute priority or independent formal verification is claimed.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-14
DOI
https://doi.org/10.5281/zenodo.23364043
Primary Topic
Geometric and Algebraic Topology
Type
preprint
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preprint

An Explicit Generating Pair for Radu's Simple Tree Lattice

Alper Ferudun
Zenodo (CERN European Organization for Nuclear Research)
Geometric and Algebraic Topology
preprint

An Explicit Generating Pair for Radu's Simple Tree Lattice

Alper Ferudun
preprint en

Abstract

We give an explicit generating pair for the torsion-free infinite simple group in Corollary IV(ii) of Radu's paper on lattices in products of trees. In the notation of that presentation, the pair is x1*x3 and x1*y3. Only the first five displayed equations are needed: a short group calculation expresses every original generator in this pair. In particular, the minimum generator number of this specific group is two. We also give a two-generator presentation with seven defining equations. This excludes one concrete candidate for a finitely presented simple group that is not two-generated; it does not resolve the general existence question. This is an unrefereed preprint. No absolute priority or independent formal verification is claimed.

Zenodo (CERN European Organization for Nuclear Research)
Geometric and Algebraic Topology
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