On small groups of finite Morley rank with a tight automorphism release_maht6aak5za4ljmxo7eq5utyfy

by Ulla Karhumäki, Pınar Uğurlu

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2021  

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 F is of positive characteristic and if -1 is a square in F^×, 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 isomorphic algebraic groups over algebraically closed fields–was developed. In this version, we have corrected typos and clarified the proofs of some lemmas.
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Date   2021-02-28
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arXiv  2012.09582v2
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