# Bad Groups

## TL;DR

This paper proves the non-existence of certain complex algebraic structures called bad groups of Morley rank 3, specifically those with an abelian Borel subgroup of rank 1, advancing understanding in model theory.

## Contribution

It establishes the non-existence of bad groups of Morley rank 3 with abelian Borel subgroups, filling a gap in the classification of such groups.

## Key findings

- No bad groups of Morley rank 3 exist with abelian Borel subgroups.
- The result extends to all Morley rank 2n+1 groups with similar properties.
- Supports the conjecture that certain algebraic groups cannot be constructed in this framework.

## Abstract

There is no bad group of Morley rank 2n+1 with an abelian Borel subgroup of Morley rank n. In particular, there is no bad group of Morley rank 3 (O. Fr{\'e}con).