Strongly Embedded Subgroups of Groups of Odd Type

TL;DR

This paper proves that certain strongly embedded subgroups in groups of finite Morley rank and odd type are solvable under specific conditions, impacting the understanding of involution centralisers and subgroup structure.

Contribution

It establishes solvability of strongly embedded subgroups in K*-groups of odd type with high Pruefer 2-rank, assuming no interpretation of bad fields, advancing group classification.

Findings

Strongly embedded subgroups are solvable if Pruefer 2-rank ≥ 2.

Groups with high normal 2-rank have trivial cores of involution centralisers.

Presence of non-solvable involution centralisers implies no proper 2-generated cores.

Abstract

In this paper we prove that any strongly embedded subgroup of a K*-group G of finite Morley rank and odd type that does not interpret any bad field is solvable if its Pruefer 2-rank is at least 2. If the normal 2-rank of G is at least 3 this has two important consequences: If G contains a non-solvable centraliser of an involution, then G does not contain any proper 2-generated core and centralisers of involutions have trivial cores.