# Regular orbits of coprime linear groups in large characteristic

## TL;DR

This paper proves that finite coprime linear groups in large characteristic have regular orbits and demonstrates the optimality of the characteristic bound, with applications to blocks with abelian defect groups.

## Contribution

It establishes the existence of regular orbits for coprime linear groups in large characteristic and shows this bound is tight, also applying results to block theory.

## Key findings

- Finite coprime linear groups in characteristic p >= (|G|-1)/2 have regular orbits.
- The bound on p is proven to be optimal.
- Application to blocks with abelian defect groups.

## Abstract

We prove that a finite coprime linear group G in characteristic p>=(|G|-1)/2 has a regular orbit. This bound on p is best possible. We also give an application to blocks with abelian defect groups.