Submission date: 1 May 2023

Abstract:

We clarify quasi-Frobenius configurations of finite Morley rank.

1. We remove one assumption in an identification theorem by Zamour while simplifying the proof.

2. We show that a strongly embedded quasi-Frobenius configuration of odd type, is actually Frobenius.

3. For dihedral configurations, one has dim G = 3 dim C.

These results rely on an interesting phenomenon of closure of non-generic matter under taking centralisers.

Mathematics Subject Classification: 20F11

Keywords and phrases: Groups of finite Morley rank; quasi-Frobenius pairs

Full text arXiv 2305.00830: pdf, ps.