Simplicity of the automorphism group of fields with operators

TL;DR

This paper proves that the automorphism group fixing all non-generic elements is simple for certain uncountable models, including strongly minimal theories and fields with operators, using adapted Lascar's proof.

Contribution

It extends Lascar's proof technique to show the simplicity of automorphism groups in a broader class of models, including fields with operators.

Findings

Automorphism groups fixing non-generic elements are simple in these models

The result applies to strongly minimal theories and fields with operators

The proof adapts Lascar's original argument for new contexts

Abstract

We adapt a proof of Lascar in order to show the simplicity of the group of automorphisms fixing pointwise all non-generic elements for a class of uncountable models of suitable theories, encompassing both strongly minimal theories as well as several theories of fields with operators.