Orbits of Automorphism Groups of Fields
نویسندگان
چکیده
This paper groups together some results that share a theme (orbits of automorphism groups on elements of a field) and some proof ideas (constructing an additive or multiplicative “trace/norm map”). Namely, we prove that a field whose automorphism group acts with finitely many orbits must be finite (Theorem 1.1), we discuss a stronger conjecture, and we show that the automorphisms of a Mal’cev-Neumann field over a field not satisfying Kaplansky’s “Hypothesis A” are all obtained by power substitutions (Theorem 3.6).
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