On the definition of Suzuki groups over rings

TL;DR

This paper defines Suzuki groups over rings using difference-algebraic groups and shows that for certain fields, this construction yields simple groups.

Contribution

It introduces a new explicit algebraic definition of Suzuki groups over rings, extending their understanding beyond fields.

Findings

Produces simple groups over fields with more than two elements

Provides an explicit difference-algebraic group description

Extends Suzuki groups to ring structures

Abstract

The definition of Suzuki groups over rings is given by means of an explicit description as a difference-algebraic group. For a (not necessarily perfect) field with more than two elements this construction produces a simple group.