Submission date: 17 December 2020

Abstract:

We consider an infinite simple group of finite Morley rank G of Prüfer 2-rank 1 which admits a tight automorphism α whose fixed-point subgroup C_G(α) is pseudofinite. We prove that C_G(α) contains a subgroup isomorphic to the Chevalley group PSL_2(F), where F is a pseudofinite field of characteristic ≠ 2. Moreover, we prove that, if a maximal split torus T of PSL_2(F) contains an involution and if F is of positive characteristic, then G ≅ PSL_2(K) for some algebraically closed field K of characteristic > 2. These results are based on the work of the second author, where a new strategy to approach the Cherlin-Zilber Conjecture--stating that infinite simple groups of finite Morley rank are algebraic groups over algebraically closed fields--was developed.

Mathematics Subject Classification: 03C20, 03C45, 20G99

Keywords and phrases:

Full text arXiv 2012.09582: pdf, ps.