Involutive automorphisms of $N_\circ^\circ$ groups of finite Morley rank

TL;DR

This paper classifies a broad class of small groups of finite Morley rank, specifically $N_ ext{circ}^ ext{circ}$-groups, by analyzing their 2-structure and providing structural insights into these infinite analogues of Thompson's $N$-groups.

Contribution

It introduces a classification of $N_ ext{circ}^ ext{circ}$-groups of finite Morley rank, focusing on their 2-structure and extending the understanding of these groups.

Findings

Classified a large class of $N_ ext{circ}^ ext{circ}$-groups

Analyzed the 2-structure of these groups

Provided structural constraints for groups with certain subgroups

Abstract

We classify a large class of small groups of finite Morley rank: $N_\circ^\circ$-groups which are the infinite analogues of Thompson's $N$-groups. More precisely, we constrain the $2$-structure of groups of finite Morley rank containing a definable, normal, non-soluble, $N_\circ^\circ$-subgroup.