Uniqueness cases in odd type groups of finite Morley rank

TL;DR

This paper investigates the structure of certain simple groups of finite Morley rank, demonstrating that a specific core leads to strong embedding and minimal connected simplicity, advancing understanding in algebraic group theory.

Contribution

It introduces a detailed analysis of 2-generated cores in minimal counterexamples, establishing their strong embedding and the minimal connected simplicity of the ambient group.

Findings

Proper 2-generated core implies strong embedding

Ambient group is minimal connected simple

Advances the classification of groups of finite Morley rank

Abstract

Here we analyze a proper 2-generated core in a minimal counter example to the Cherlin-Zilber Algebraicity Conjecture for simple groups of finite Morley rank. We ultimately show that such a group is strongly embedded and the ambiant group is minimal connected simple.