Small groups of finite Morley rank with a supertight automorphism

Ulla Karhumäki; Pınar Uğurlu

Small groups of finite Morley rank with a supertight automorphism

Group Theory 2023-09-22 v5 Logic

Authors: Ulla Karhumäki , Pınar Uğurlu

Abstract

Let $G$ be an infinite simple group of finite Morley rank and of Pr\"{u}fer $2$ -rank $1$ which admits a supertight automorphism $\alpha$ such that the fixed-point subgroup $C_G(\alpha^n)$ is pseudofinite for all integers $n > 0$ . We prove that $G \cong {\rm PGL}_2(K)$ for some algebraically closed field $K$ of characteristic $\neq 2$ .

Keywords

finite morley rank supertight automorphism simple group prüfer 2-rank pseudofinite pgl2

Cite

@article{arxiv.2012.09582,
  title  = {Small groups of finite Morley rank with a supertight automorphism},
  author = {Ulla Karhumäki and Pınar Uğurlu},
  journal= {arXiv preprint arXiv:2012.09582},
  year   = {2023}
}

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