On Frattini arguments in L-groups of finite Morley rank

TL;DR

This paper extends the understanding of Carter subgroups in groups of finite Morley rank by modifying existing constructions to establish invariance properties, reducing reliance on conjugacy assumptions.

Contribution

It introduces a modified construction of Carter subgroups that demonstrates their invariance under Sylow 2-subgroups in degenerate type groups.

Findings

Carter subgroups can be made invariant under Sylow 2-subgroups.

Reduces the need to prove conjugacy of Carter subgroups in degenerate groups.

Provides a new approach to analyzing automorphism-invariant subgroups.

Abstract

We modify the Frecon-Jaligot construction of Carter subgroups to show that a degenerate type group has a Carter subgroup invariant under the Sylow 2-subgroup of a group of automorphisms; thus reducing the need to know that Carter subgroups are conjugate in degenerate type groups.