منابع مشابه
Fixed Points of Zircon Automorphisms
A zircon is a poset in which every principal order ideal is finite and equipped with a so-called special matching. We prove that the subposet induced by the fixed points of any automorphism of a zircon is itself a zircon. This provides a natural context in which to view recent results on Bruhat orders on twisted involutions in Coxeter groups. 1. Background and results Let P be a partially order...
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motivated by a celebrated theorem of schur, we show that if~$gamma$ is a normal subgroup of the full automorphism group $aut(g)$ of a group $g$ such that $inn(g)$ is contained in $gamma$ and $aut(g)/gamma$ has no uncountable abelian subgroups of prime exponent, then $[g,gamma]$ is finite, provided that the subgroup consisting of all elements of $g$ fixed by $gamma$ has finite index. so...
متن کاملFixed Points of Involutive Automorphisms of the Bruhat Order
Applying a classical theorem of Smith, we show that the poset property of being Gorenstein∗ over Z2 is inherited by the subposet of fixed points under an involutive poset automorphism. As an application, we prove that every interval in the Bruhat order on (twisted) involutions in an arbitrary Coxeter group has this property, and we find the rank function. This implies results conjectured by F. ...
متن کاملFixed points of automorphisms of real algebraic curves
We bound the number of fixed points of an automorphism of a real curve in terms of the genus and the number of connected components of the real part of the curve. Using this bound, we derive some consequences concerning the maximum order of an automorphism and the maximum order of an abelian group of automorphisms of a real curve. We also bound the full group of automorphisms of a real hyperell...
متن کاملFrobenius groups of automorphisms and their fixed points
Suppose that a finite group G admits a Frobenius group of automorphisms FH with kernel F and complement H such that the fixed-point subgroup of F is trivial: CG(F ) = 1. In this situation various properties of G are shown to be close to the corresponding properties of CG(H). By using Clifford’s theorem it is proved that the order |G| is bounded in terms of |H| and |CG(H)|, the rank of G is boun...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.2307/2040825