Infinite transitivity for automorphism groups of the affine plane

TL;DR

This paper investigates conditions under which automorphism groups of the affine plane act infinitely transitively, focusing on subgroups generated by one-parameter additive groups, and provides a comprehensive criterion for this property.

Contribution

It establishes a necessary and sufficient condition for infinite transitivity of algebraically generated automorphism groups of the affine plane, especially those generated by one-parameter additive groups.

Findings

Characterization of infinite transitivity for certain automorphism subgroups

Necessary and sufficient condition derived for subgroups generated by additive groups

Enhanced understanding of automorphism group actions on the affine plane

Abstract

This paper is dedicated to the problem of infinite transitivity for algebraically generated automorphism groups of the affine plane. We provide a necessary and sufficient condition of infinite transitivity for a large family of subgroups generated by one-parameter additive groups.