Cosets, genericity, and the Weyl group

TL;DR

This paper establishes a non-generosity property for proper cosets in groups of finite Morley rank and explores the theory of Weyl groups within this framework, advancing understanding of their structure and behavior.

Contribution

It introduces a non-generosity theorem for proper cosets and develops the theory of Weyl groups in groups of finite Morley rank, providing new insights into their algebraic properties.

Findings

Proper cosets are non-generous in groups of finite Morley rank.

Develops the theory of Weyl groups in this context.

Provides structural results on these groups.

Abstract

We prove a non-generosity theorem for proper cosets in groups of finite Morley rank and elaborate on the theory of Weyl groups in this context.