Some finiteness results on triangular automorphisms

TL;DR

This paper proves that any finite set of connected algebraic subgroups within the triangular automorphisms group generates a connected solvable subgroup, advancing understanding of the structure of these automorphism groups.

Contribution

It establishes a finiteness property showing finite collections generate connected solvable subgroups in the triangular automorphisms group.

Findings

Finite collections generate connected solvable subgroups

Advances structural understanding of automorphism groups

Provides finiteness results for algebraic subgroup generation

Abstract

In this note we prove that every finite collection of connected algebraic subgroups of the group of triangular automorphisms of the affine space generates a connected solvable algebraic subgroup.