Minimal connected simple groups of finite Morley rank with strongly embedded subgroups

TL;DR

This paper investigates minimal nonalgebraic simple groups of finite Morley rank, establishing a bound on their Prufer rank and refining previous classifications by removing the tameness assumption.

Contribution

It introduces a new approach using strongly embedded subgroups and 0-unipotence machinery to analyze minimal simple groups, improving upon prior work by Cherlin and Jaligot.

Findings

Prufer rank of minimal nonalgebraic simple groups is at most 2

Eliminates the tameness assumption from previous classifications

Uses 0-unipotence machinery to analyze Borel subgroup intersections

Abstract

We show that a minimal nonalgebraic simple groups of finite Morley rank has Prufer rank at most 2, and eliminates tameness from Cherlin and Jaligot's past work on minimal simple groups. The argument given here begins with the strongly embedded minimal simple configuration of Borovik, Burdges and Nesin. The 0-unipotence machinery of Burdges's thesis is used to analyze configurations involving nonabelian intersections of Borel subgroups. The number theoretic punchline of Cherlin and Jaligot has been replaced with a new genericity argument.