On a Boundary Point Repelling 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...
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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In this paper, we study the minimality of the boundary of a Coxeter system. We show that for a Coxeter system (W,S) if there exist a maximal spherical subset T of S and an element s0 ∈ S such that m(s0, t) ≥ 3 for each t ∈ T and m(s0, t0) = ∞ for some t0 ∈ T , then every orbit Wα is dense in the boundary ∂Σ(W,S) of the Coxeter system (W,S), hence ∂Σ(W,S) is minimal, where m(s0, t) is the order ...
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Preface A famous theorem by Frobenius in 1901 proves that if a group G contains a proper non trivial subgroup H such that H ∩ g −1 Hg = {1 G } for all g ∈ G \ H, then there exists a normal subgroup N such that G is the semidirect product of N and H. Groups with this property-the so called Frobenius groups-arise in a natural way as transitive permutation groups, but they can also be characterize...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1993
ISSN: 0022-247X
DOI: 10.1006/jmaa.1993.1362