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71.
给出了Rn上的线性同构和线性流具有极限跟踪性的特征:线性同构具有极限跟踪性当且仅当其对应的矩阵为双曲的;线性流具有极限跟踪性当且仅当其对应矩阵的所有特征根均具有非零实部. 相似文献
72.
P. Shumyatsky’s question 11.126 in the “Kourovka Notebook” is answered in the affirmative: it is proved that there exist a
constant c and a function of a positive integer argument f(m) such that if a finite group G admits an automorphism ϕ of order
4 having exactly m fixed points, then G has a normal series G ⩾ H ⩽ N such that |G/H| ⩽ f(m), the quotient group H/N is nilpotent
of class ⩽ 2, and the subgroup N is nilpotent of class ⩽ c (Thm. 1). As a corollary we show that if a locally finite group
G contains an element of order 4 with finite centralizer of order m, then G has the same kind of a series as in Theorem 1.
Theorem 1 generalizes Kovács’ theorem on locally finite groups with a regular automorphism of order 4, whereby such groups
are center-by-metabelian. Earlier, the first author proved that a finite 2-group with an almost regular automorphism of order
4 is almost center-by-metabelian. The proof of Theorem 1 is based on the authors’ previous works dealing in Lie rings with
an almost regular automorphism of order 4. Reduction to nilpotent groups is carried out by using Hall-Higman type theorems.
The proof also uses Theorem 2, which is of independent interest, stating that if a finite group S contains a nilpotent subgroup
T of class c and index |S: T | = n, then S contains also a characteristic nilpotent subgroup of class ⩽ c whose index is bounded
in terms of n and c. Previously, such an assertion has been known for Abelian subgroups, that is, for c = 1.
__________
Translated from Algebra i Logika, Vol. 45, No. 5, pp. 575–602, September–October, 2006. 相似文献
73.
V. S. Samovol 《Mathematical Notes》2002,71(3-4):538-549
This paper deals with problems related to local smooth transformations of ordinary differential equations preserving linear automorphisms of these equations. 相似文献
74.
Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that [x^σ,x] E Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R)=2 and dimc RC = 4. 相似文献
75.
Alexander V. karabegov 《Letters in Mathematical Physics》2004,70(1):43-56
To each natural star product on a Poisson manifold M we associate an antisymplectic involutive automorphism of the formal neighborhood of the zero section of the cotangent bundle of M. If M is symplectic, this mapping is shown to be the inverse mapping of the formal symplectic groupoid of the star product. The construction of the inverse mapping involves modular automorphisms of the star product. 相似文献
76.
Bubble-Sort图和Modified Bubble-Sort图是两类特殊的Cayley图,由于其在网络构建中的应用而受到广泛关注.本文完全确定了这两类图的自同构群. 相似文献
77.
运用基图自同构能被提升的线性准则 ,对满足 :1覆叠变换群 K =Znp,2覆盖图的保簇变换群是点传递的 Petersen图的连通正则覆盖图进行了完全分类 .这种图共有 1 2种类型 . 相似文献
78.
We compare Aut(Q), the classical automorphism group of a countable dense linear order, with Aut
c
(Q), the group of all computable automorphisms of such an order. They have a number of similarities, including the facts that every element of each group is a commutator and each group has exactly three nontrivial normal subgroups. However, the standard proofs of these facts in Aut(Q) do not work for Aut
c
(Q). Also, Aut(Q) has three fundamental properties which fail in Aut
c
(Q): it is divisible, every element is a commutator of itself with some other element, and two elements are conjugate if and only if they have isomorphic orbital structures. 相似文献
79.
本文给出了有向循环图可分解为圈的直积的一个充分条件,基于这一结果,讨论了它们的哈密顿性及自同构群。 相似文献
80.
Explicit examples of finite subgroups of the group of homotopy classes of self-homotopy equivalences of some flat Riemannian manifolds which cannot be lifted to effective actions are given. It is also shown that no finite subgroups of the kernel of π0(Homeo(M))→Out π1(M) can be lifted back to Homeo(M), for a large class of flat manifolds M. Some results of an earlier paper by the authors are refined and related to recent work of R. Schoen and S.T. Yau. 相似文献