Fields of invariants of finite linear groups

TL;DR

This paper surveys the rationality problem for finite linear groups, focusing on low-dimensional cases, particularly four-dimensional groups, to understand their fields of invariants.

Contribution

It provides a comprehensive overview of the rationality question for finite linear groups, emphasizing the four-dimensional case, which is less understood.

Findings

Analysis of rationality in four-dimensional cases

Identification of key invariants in finite linear groups

Summary of known results and open problems

Abstract

The survey is devoted to the rationality question of finite linear groups. We concentrate on lower-dimensional cases, especially on the case of dimension four.