arXiv subjects
Publications and source records attributed to Tuna Altinel.
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.
A sharply 2-transitive permutation group of finite Morley rank and characteristic 2 splits; a split sharply 2-transitive permutation group of finite Morley rank and characteristic different from 2 is the group of affine transformations of an algebraically closed field. In particular, a sharply 2-transitive permutation group of finite Morley rank of characteristic 3 is the group of affine transformations of an algebraically closed field of characteristic 3. Without any assumption on Morley rank, a sharply 2-transitive permutation group of characteristic 0 splits if its point stabilizers are virtually abelian.
We prove a Jordan decomposition theorem for minimal connected simple groups of finite Morley rank with non-trivial Weyl group. From this, we deduce a precise structural description of Borel subgroups of this family of simple groups. Along the way we prove a Tetrachotomy theorem that classifies minimal connected simple groups. Some of the techniques that we develop help us obtain a simpler proof of a theorem of Burdges, Cherlin and Jaligot.
We prove that in a connected group of finite Morley rank the centralizers of decent tori are connected. We then apply this result to the analysis of minimal connected simple groups of finite Morley rank. Our applications include general covering properties by Borel subgroups, the description of Weyl groups and the analysis of toral automorphisms.