Finite groups with only small automorphism orbits
نویسندگان
چکیده
منابع مشابه
Orbits of Automorphism Groups of Fields
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-N...
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متن کاملComments on " Orbits of Automorphism Groups of Fields "
Let R be a commutative k−algebra over a field k. Assume R is a Noetherian integral domain and |R| = ∞. The group of k−automorphisms of R,i.e., Autk(R) acts in a natural way on (R − k). We study the structure of R when orbit space (R−k)/Autk(R) is finite, and note that most of the results proved in [1, §2] hold in this case as well. We also give an elementary proof of [1,Theorem 1.1] in case k i...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2020
ISSN: 1435-4446,1433-5883
DOI: 10.1515/jgth-2019-0152