An Explicit Generating Pair for Radu’s Simple Tree Lattice
Manuscript 14 October 2026 · Online 14 October 2026
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. The pair is \(x_1x_3\) and \(x_1y_3\). A short group calculation using only the first five displayed equations recovers every original generator. Thus this specific group has minimum generator number 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; the general existence question remains unresolved. Simplicity and geometric structure are credited to Radu. The preprint is unrefereed and AI-assisted; no absolute priority, independent review or formal verification is claimed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete scoped proof
- Categories
- math.GR
- Manuscript
- 14 October 2026
- Online release
- 14 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “An Explicit Generating Pair for Radu's Simple Tree Lattice,” EulerSolve Research Papers, AIM-GEOMETRIC_GROUP_THEORY-0126, 2026. https://doi.org/10.5281/zenodo.23364044.
BibTeX
@misc{ferudun2026radugenerators,
author = {Ferudun, Alper},
title = {An Explicit Generating Pair for Radu's Simple Tree Lattice},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-geometric-group-theory-0126/},
doi = {10.5281/zenodo.23364044},
note = {AIM-GEOMETRIC_GROUP_THEORY-0126; unrefereed preprint}
}