# Elements generating a proper normal subgroup of the Cremona group

## TL;DR

This paper characterizes infinite order elements in the Cremona group over an algebraically closed field whose non-zero powers generate proper normal subgroups, advancing understanding of the group's structure.

## Contribution

It provides a complete characterization of certain infinite order elements related to proper normal subgroups in the Cremona group.

## Key findings

- Identifies conditions under which elements generate proper normal subgroups
- Classifies infinite order elements with this property
- Enhances understanding of the Cremona group's subgroup structure

## Abstract

Consider an algebraically closed field k and the Cremona group of all birational transformations of the projective plane over k. We characterize infinite order elements of this group having a non-zero power generating a proper normal subgroup of the Cremona group.