Bad groups in the sense of Cherlin

TL;DR

This paper discusses the non-existence of 'bad groups' of Morley rank 3, establishing that all such simple groups are isomorphic to PSL2(K) over an algebraically closed field.

Contribution

It proves that no 'bad groups' of Morley rank 3 exist, confirming they are all isomorphic to PSL2(K).

Findings

All simple groups of Morley rank 3 are isomorphic to PSL2(K).

No 'bad groups' of Morley rank 3 exist.

Supports the Cherlin-Zilber conjecture for rank 3 groups.

Abstract

There exists no bad group (in the sense of Gregory Cherlin), namely any simple group of Morley rank 3 is isomorphic to PSL2(K) for an algebraically closed field K.