Lie rank in groups of finite Morley rank with solvable local subgroups

TL;DR

This paper establishes a dichotomy for groups of finite Morley rank with solvable local subgroups and high Pr"ufer p-rank, showing they either have p-strong embedding or a specific Pr"ufer p-rank value.

Contribution

It introduces a general dichotomy theorem for such groups, advancing understanding of their structural properties.

Findings

Either the group admits p-strong embedding or Pr"ufer p-rank equals 2.

Provides a classification criterion based on Pr"ufer p-rank.

Enhances the structural theory of groups of finite Morley rank.

Abstract

We prove a general dichotomy theorem for groups of finite Morley rank with solvable local subgroups and of Pr\"ufer p-rank at least 2, leading either to some p-strong embedding, or to the Pr\"ufer p-rank being exactly 2.