具有超紧自同构的有限莫利秩小群

关于通用和超紧自同构

On generic and supertight automorphisms

本文研究稳定群的通用自同构的超紧性质，证明其存在性，并探讨超紧自同构与基础域的关联，支持固定点伪有限性原理。

超紧自同构的不动点子群

Fixed point subgroups of a supertight automorphism

研究有限 Morley 秩无限单群的超紧自同构，证明其各次幂不动点子群相对伪有限 Chevalley 基座的指数一致有界，而基座的 Sylow 2-子群大小无界，并说明相关识别结果无需 CFSG。

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

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.

On analogies between algebraic groups and groups of finite Morley rank

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.

On Frattini arguments in L-groups of finite Morley rank

We modify the Frecon-Jaligot construction of Carter subgroups to show that a degenerate type group has a Carter subgroup invariant under the Sylow 2-subgroup of a group of automorphisms; thus reducing the need to know that Carter subgroups are conjugate in degenerate type groups.

Pseudofinite groups as fixed points in simple groups of finite Morley rank

We prove that if the group of fixed points of a generic automorphism of a simple group of finite Morley rank is pseudofinite, then this group is an extension of a (twisted) Chevalley group over a pseudofinite field. On the way to obtain this result, we classify non-abelian definably simple pseudofinite groups of finite centralizer dimension (using the ideas of John S. Wilson).