On small groups of finite Morley rank with a tight automorphism
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by
Ulla Karhumäki, Pınar Uğurlu
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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