Constructing arithmetic subgroups of unipotent groups

TL;DR

This paper presents an algorithm to find generators for arithmetic subgroups of unipotent groups, based on a new proof of their finite generation, extending classical results to a broader context.

Contribution

It introduces a novel algorithm for constructing generators of G(Z) for unipotent algebraic groups G over Q, with a new proof of finite generation.

Findings

Algorithm successfully computes generators for G(Z)

Provides a new proof of finite generation for these subgroups

Extends classical results to more general unipotent groups

Abstract

Let G be a unipotent algebraic subgroup of some GL_m(C) defined over Q. We describe an algorithm for finding a finite set of generators of the subgroup G(Z) = G \cap GL_m(Z). This is based on a new proof of the result (in more general form due to Borel and Harish-Chandra) that such a finite generating set exists.