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The main result of the paper is the following theorem. Let q be a prime, n a positive integer, and A an elementary abelian group of order q2. Suppose that A acts coprimely on a finite group G and assume that for each \({a \in A^{\#}}\) every element of CG(a) is n-Engel in G. Then the group G is k-Engel for some \({\{n,q\}}\)-bounded number k. 相似文献
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Marco Abate 《Mathematische Annalen》1989,283(4):645-655
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Jasmin Raissy 《Mathematische Zeitschrift》2010,264(4):881-900
Let f be a germ of holomorphic diffeomorphism of mathbb Cn{mathbb {C}^{n}} fixing the origin O, with d f O diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of d f O and some restrictions on the resonances, f is locally holomorphically linearizable if and only if there exists a particular f -invariant complex manifold. Most of the classical linearization results can be obtained as corollaries of our result. 相似文献
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Pavel Shumyatsky 《Proceedings of the American Mathematical Society》2001,129(12):3479-3484
Let be a prime, and let be a finite -group acted on by an elementary abelian -group . The following results are proved:
1. If and is nilpotent of class at most for any , then the group is nilpotent of -bounded class.
2. If and is nilpotent of class at most for any , then the derived group is nilpotent of -bounded class.
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Pavel Shumyatsky 《Journal of Pure and Applied Algebra》2011,215(11):2559-2566
Suppose that a Frobenius group FH with cyclic kernel F and complement H acts on a finite group G in such a manner that CG(F)=1 and CG(H) satisfies a positive law of degree k. It is shown that G satisfies a positive law of degree that is bounded solely in terms of k and |FH|. 相似文献
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Oblatum 21-IX-1991 & 30-IV-1992 相似文献
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Marina Levenshtein Simeon Reich 《Nonlinear Analysis: Theory, Methods & Applications》2009,70(12):4145-4150
We approximate fixed points of holomorphic and ρ-nonexpansive self-mappings of the Hilbert ball using both continuous and discrete schemes. 相似文献
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Translated from Algebra i Logika, Vol. 30, No. 6, pp. 735–746, November–December, 1991. 相似文献
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Zhang Guangyuan 《中国科学A辑(英文版)》2001,44(3):330-337
Let Δυ be the unit ball in ℂυ with center 0 (the origin of υ) and let F:Δυ→ℂυbe a holomorphic map withF(0) = 0. This paper is to study the fixed point multiplicities at the origin 0 of the iteratesF
i
=F∘⋯∘F (i times),i = 1,2,.... This problem is easy when υ = 1, but it is very complicated when υ > 1. We will study this problem generally. 相似文献
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In this paper, we study the local structure of the fixed point set of a holomorphic mapping defined on a (not necessarily bounded or convex) domain in a complex Banach space, using ergodic theory of linear operators and the nonlinear numerical range introduced by L. A. Harris. We provide several constructions of holomorphic retractions and a generalization of Cartan’s Uniqueness Theorem. We also estimate the deviation of a holomorphic mapping from its linear approximation, the Fréchet derivative at a fixed point. 相似文献
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Chiara de Fabritiis 《Proceedings of the American Mathematical Society》1996,124(10):3027-3037
We give a complete classification of the holomorphic self-maps of the unit ball of into itself which commute with a given hyperbolic automorphism.
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The number of fixed points of a random permutation of {1,2,…,n} has a limiting Poisson distribution. We seek a generalization, looking at other actions of the symmetric group. Restricting
attention to primitive actions, a complete classification of the limiting distributions is given. For most examples, they
are trivial – almost every permutation has no fixed points. For the usual action of the symmetric group on k-sets of {1,2,…,n}, the limit is a polynomial in independent Poisson variables. This exhausts all cases. We obtain asymptotic estimates in
some examples, and give a survey of related results.
This paper is dedicated to the life and work of our colleague Manfred Schocker.
We thank Peter Cameron for his help. Diaconis was supported by NSF grant DMS-0505673. Fulman received funding from NSA grant
H98230-05-1-0031 and NSF grant DMS-0503901. Guralnick was supported by NSF grant DMS-0653873. This research was facilitated
by a Chaire d’Excellence grant to the University of Nice Sophia-Antipolis. 相似文献
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