Small groups of finite Morley rank with a supertight automorphism

Let G be an infinite simple group of finite Morley rank and of Pr & uuml;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. The main result of this paper is the identification of G with PGL 2 ( K ) for some algebraically closed field K of characteristic not equal 2. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).