On quasi-Frobenius pairs of finite Morley rank

Altınel, Tuna; Corredor, Luis Jaime; Deloro, Adrien

doi:10.1090/proc/16771

On quasi-Frobenius pairs of finite Morley rank
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by Tuna Altınel, Luis Jaime Corredor and Adrien Deloro;

Proc. Amer. Math. Soc. 152 (2024), 2791-2804

DOI: https://doi.org/10.1090/proc/16771

Published electronically: May 21, 2024

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Abstract:

[$\bullet$]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.
[$\bullet$]Besides contributing to the Cherlin-Zilber conjecture, we believe the topic of quasi-Frobenius pairs deserves general attention from the group theory community.

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