Semisimple torsion in groups of finite Morley rank

TL;DR

This paper investigates the structure of groups with finite Morley rank lacking unipotent p-torsion, establishing key properties about p-torsion placement, Sylow p-subgroups, and prime divisors, aiding classification efforts.

Contribution

It proves that p-torsion resides within tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of the Weyl group approximation, advancing the understanding of these groups.

Findings

p-torsion occurs inside tori

Sylow p-subgroups are conjugate

p is not the minimal prime divisor of the Weyl group

Abstract

We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the ``Weyl group.'' These results are quickly finding extensive applications within the classification project.