Elementary groups in $\PSL(3,\C)$

TL;DR

This paper classifies elementary subgroups of PSL(3,C) acting on complex projective plane with finitely many lines in their Kulkarni limit set, advancing understanding of their geometric and group-theoretic properties.

Contribution

It provides a complete classification of elementary subgroups of PSL(3,C) with specific limit set configurations, a previously unresolved problem.

Findings

Classified elementary subgroups with finitely many lines in limit set

Identified geometric configurations of limit sets in complex projective plane

Enhanced understanding of subgroup actions in PSL(3,C)

Abstract

In this paper, we give a classification of the subgroups of $\textrm{PSL}(3, \mathbb{C})$ that act on $\mathbb{P}_{\mathbb{C}}^2$ in such a way that their Kulkarni limit set has finitely many lines in general position lines. These are the elementary groups.