Involutions in groups of finite Morley rank of degenerate type

TL;DR

This paper extends the Feit-Thompson theorem to simple groups of finite Morley rank, showing that if such a group has a finite Sylow 2-subgroup, then its Sylow 2-subgroup is trivial, advancing understanding of their structure.

Contribution

It proves a key structural result for simple groups of finite Morley rank, linking the finiteness of Sylow 2-subgroups to their triviality, akin to the classical Feit-Thompson theorem.

Findings

Connected groups of finite Morley rank with finite Sylow 2-subgroups have trivial Sylow 2-subgroups.

The result parallels the Feit-Thompson theorem for finite groups.

Provides new insights into the structure of groups of finite Morley rank.

Abstract

This article proves a version of the Feit-Thompson theorem for simple groups of finite Morley rank: a connected groups of finite Morley rank with a finite Sylow 2-subgroup has a trivial Sylow 2-subgroups.