共查询到20条相似文献,搜索用时 78 毫秒
1.
Gadi Moran 《Journal of Combinatorial Theory, Series A》1982,33(1):82-98
A conjugacy class in the infinite-symmetric group is said to have parity features if no finitary odd permutation is a product of two of its members. The conjugacy classes having parity features are determined. The role played by a property of this kind in determining products of conjugacy classes in any group in which every element is conjugate with its inverse is studied. 相似文献
2.
F. C. Holroyd 《Discrete Mathematics》1992,110(1-3):283-287
A finite group G is said to be action reconstructible if, for any action of G on a finite set, the numbers of orbits under restriction to each subgroup always give enough information to reconstruct the action up to equivalence. G is character reconstructible if, given any matrix representation of G, the mean value of the character on each subgroup always gives enough information to reconstruct the character. The conjugacy matrix of G is the matrix whose (ij) entry is the number of elements of the jth conjugacy class belonging to a typical subgroup of the ith subgroup conjugacy class. It is shown that G is action reconstructible if and only if the rows of this matrix are linearly independent (which is in turn true if and only if G is cyclic), and is character reconstructible if and only if the columns are linearly independent (which is true if and only if any two elements of G which generate conjugate cyclic subgroups are themselves conjugate). 相似文献
3.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》2003,43(2):61-71
Subsets 𝒜, 𝒮 of an additive group G are complementary if 𝒜 + 𝒮 = G. When 𝒜 is of finite cardinality ∣𝒜∣, and G is ℤ or ℝ, we give sufficient conditions for the existence of a complementary set 𝒮 with “density” not much larger than
1/∣𝒜∣. 相似文献
4.
Wolfgang M. Schmidt 《Monatshefte für Mathematik》2003,138(1):61-71
Subsets 𝒜, 𝒮 of an additive group G are complementary if 𝒜 + 𝒮 = G. When 𝒜 is of finite cardinality ∣𝒜∣, and G is ℤ or ℝ, we give sufficient conditions for the existence of a complementary set 𝒮 with “density” not much larger than
1/∣𝒜∣.
Supported in part by NSF DMS-0074531.
Received February 14, 2002; in revised form July 18, 2002
RID="a"
ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday 相似文献
5.
Z. I. Borevich E. V. Dybkova L. Yu. Kolotilina 《Journal of Mathematical Sciences》1981,17(4):1945-1951
For the full linear group over a matrix-local ring whose quotient by the Jacobson radical is not the field of two elements, we settle the question of the conjugacy ofD -net subgroups (Ref. Zh. Mat., 1977, 2A280). TwoD -net subgroups are conjugate if and only if theD -nets defining them are similar (i.e., can be transformed into each other by a permutation matrix). An analogous result is obtained forD -net subgroups of the symplectic group over a commutative local ring whose residue field contains more than three elements.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 86, pp. 11–18, 1979. 相似文献
6.
D. O. Revin 《Siberian Mathematical Journal》2011,52(5):904-913
Given a set π of primes, say that a finite group G satisfies the Sylow π-theorem if every two maximal π-subgroups of G are conjugate; equivalently, the full analog of the Sylow theorem holds for π-subgroups. Say also that a finite group G satisfies the Baer-Suzuki π-theorem if every conjugacy class of G every pair of whose elements generate a π-subgroup itself generates a π-subgroup. In this article we prove, using the classification of finite simple groups, that if a finite group satisfies the
Sylow π-theorem then it satisfies the Baer-Suzuki π-theorem as well. 相似文献
7.
P. Christopher Staecker 《Journal of Pure and Applied Algebra》2011,215(7):1702-1710
We give two results for computing doubly-twisted conjugacy relations in free groups with respect to homomorphisms φ and ψ such that certain remnant words from φ are longer than the images of generators under ψ.Our first result is a remnant inequality condition which implies that two words u and v are not doubly-twisted conjugate. Further we show that if ψ is given and φ, u, and v are chosen at random, then the asymptotic probability that u and v are not doubly-twisted conjugate is 1. In the particular case of singly-twisted conjugacy, this means that if φ, u, and v are chosen at random, then u and v are not in the same singly-twisted conjugacy class with asymptotic probability 1.Our second result generalizes Kim’s “bounded solution length”. We give an algorithm for deciding doubly-twisted conjugacy relations in the case where φ and ψ satisfy a similar remnant inequality. In the particular case of singly-twisted conjugacy, our algorithm suffices to decide any twisted conjugacy relation if φ has remnant words of length at least 2.As a consequence of our generic properties we give an elementary proof of a recent result of Martino, Turner, and Ventura, that computes the densities of the sets of injective and surjective homomorphisms from one free group to another. We further compute the expected value of the density of the image of a homomorphism. 相似文献
8.
Hung P. Tong-Viet 《Acta Mathematica Hungarica》2013,140(1-2):105-116
Let G be a finite group. An x∈G is a real element if x and x ?1 are conjugate in G. For x∈G, the conjugacy class x G is said to be a real conjugacy class if every element of x G is real. We show that if 4 divides no real conjugacy class sizes of a finite group G, then G is solvable. We also study the structure of such groups in detail. This generalizes several results in the literature. 相似文献
9.
S. M. Shimorin 《Journal of Mathematical Sciences》1997,87(5):3912-3924
An explicit integral formula is obtained for the Green function of the weighted biharmonic operator Δ(1−∣z∣2)−αΔ in the unit disk of the complex plane for the case α ∈ (−1, 0). The formula shows the positivity of the Green function.
This is a basis for a theorem on factorization of analytic functions in the weighted Bergman spaces with the weights ω(z)=(1−∣z∣2)α as products of a nonvanishing function and a function of special form responsible for the zeros. Bibliography: 16 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1995, pp. 203–221. 相似文献
10.
Guy Alfandary 《Israel Journal of Mathematics》1994,86(1-3):211-220
LetG be a finite group. Attach toG the following two graphs: Γ — its vertices are the non-central conjugacy classes ofG, and two vertices are connected if their sizes arenot coprime, and Γ* — its vertices are the prime divisors of sizes of conjugacy classes ofG, and two vertices are connected if they both divide the size of some conjugacy class ofG. We prove that whenever Γ* is connected then its diameter is at most 3, (this result was independently proved in [3], for
solvable groups) and Γ* is disconnected if and only ifG is quasi-Frobenius with abelian kernel and complements. Using the method of that proof we give an alternative proof to Theorems
in [1],[2],[6], namely that the diameter of Γ is also at most 3, whenever the graph is connected, and that Γ is disconnected
if and only ifG is quasi-Frobenius with abelian kernel and complements. As a result we conclude that both Γ and Γ* have at most two connected
components. In [2],[3] it is shown that the above bounds are best possible.
The content of this paper corresponds to a part of the author’s Ph.D. thesis carried out at the Tel Aviv University under
the supervision of Prof. Marcel Herzog. 相似文献
11.
Although the conjugacy classes of the general linear group are known, it is not obvious (from the canonic form of matrices) that two permutation matrices are similar if and only if they are conjugate as permutations in the symmetric group, i.e., that conjugacy classes of S n do not unite under the natural representation. We prove this fact, and give its application to the enumeration of fixed points under a natural action of S n × S n . We also consider the permutation representations of S n which arise from the action of S n on ordered tuples and on unordered subsets, and classify which of them unite conjugacy classes and which do not. 相似文献
12.
Shi Rong LI 《数学学报(英文版)》2005,21(4):797-802
For a finite group G, let T(G) denote a set of primes such that a prime p belongs to T(G) if and only if p is a divisor of the index of some maximal subgroup of G. It is proved that if G satisfies any one of the following conditions: (1) G has a p-complement for each p∈T(G); (2)│T(G)│= 2: (3) the normalizer of a Sylow p-subgroup of G has prime power index for each odd prime p∈T(G); then G either is solvable or G/Sol(G)≌PSL(2, 7) where Sol(G) is the largest solvable normal subgroup of G. 相似文献
13.
Saman Babaie-Kafaki 《Journal of Optimization Theory and Applications》2012,154(3):916-932
In order to take advantage of the attractive features of Polak–Ribière–Polyak and Fletcher–Reeves conjugate gradient methods, two hybridizations of these methods are suggested, using a quadratic relaxation of a hybrid conjugate gradient parameter proposed by Gilbert and Nocedal. In the suggested methods, the hybridization parameter is computed based on a conjugacy condition. Under proper conditions, it is shown that the proposed methods are globally convergent for general objective functions. Numerical results are reported; they demonstrate the efficiency of one of the proposed methods in the sense of the performance profile introduced by Dolan and Moré. 相似文献
14.
We investigate the uniform piecewise linearizing question for a family of Lorenz maps. Let f be a piecewise linear Lorenz map with different slopes and positive topological entropy, we show that f is conjugate to a linear mod one transformation and the conjugacy admits a dichotomy: it is either bi-Lipschitz or singular depending on whether f is renormalizable or not. f is renormalizable if and only if its rotation interval degenerates to be a rational point. Furthermore, if the endpoints are periodic points with the same rotation number, then the conjugacy is quasisymmetric. 相似文献
15.
THE ASYMPTOTIC THEORY OF INITIAL VALUEPROBLEMS FOR SEMILINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS 总被引:10,自引:0,他引:10
LAISHAOYONG MuCHUNLAI 《高校应用数学学报(英文版)》1997,12(3):321-332
This paper deals with the asymptotic theory of initial value problems for semilinear waveequations in three space dimensions. The well-posedness and validity of formal approximations ona long time scale of order |ε|^-1 are discussed in the classical sense of C^2 This result describes aceu-ratively the approximations of solutions. At the end of this paper an application of the asymptotictheory is given to analyze a special model for a perturbed wave equation, 相似文献
16.
O. Yu. Teplins’kyi 《Ukrainian Mathematical Journal》2011,62(8):1267-1284
We prove the existence of two real-analytic diffeomorphisms of the circle with break of the same size and an irrational rotation
number of semibounded type that are not C
1+γ
-smoothly conjugate for any γ > 0. In this way, we show that the previous result concerning the C
1-smoothness of conjugacy for these mappings is the exact estimate of smoothness for this conjugacy. 相似文献
17.
In this paper we show there is exactly one conjugacy class of subgroups ofE
6(ℂ) isomorphic toL(2, 13) with each of the characters 13+14 and 1+12+14 on a 27-dimensional module forE
6. The one with character 13+14 is a subgroup of the irreducible closed subgroup of typeG
2. There is a unique conjugacy class for each of the three algebraic conjugate characters 1+12+14. Our arguments have applications
to fields of characteristic prime to |L(2, 13)|.
Dedicated to John Thompson for his keen interest in broad areas of mathematics and in mathematicians 相似文献
18.
We characterize irreducible Hermitian symmetric spaces which are not of tube type, both in terms of
the topology of the space of triples of pairwise transverse points in the Shilov boundary, and of two invariants which we
introduce, the Hermitian triple product and its complexification. We apply these results and the techniques introduced in
[6] to characterize conjugacy classes of Zariski dense representations of a locally compact group into the connected component
G of the isometry group of an irreducible Hermitian symmetric space which is not of tube type, in terms of the pullback of
the bounded Kahler class via the representation. We conclude also that if the second bounded cohomology of a finitely generated
group Γ is finite dimensional, then there are only finitely many conjugacy classes of representations of Γ into G with Zariski
dense image. This generalizes results of [6]. 相似文献
19.
A group G is said to be a group with Černikov conjugacy classes or a CC-group if it induces on the normal closure of each
one of its elements a group of automorphisms which is a Černikov group, that is, a finite extension of an abelian group satisfying
the minimal condition on subgroups. This concept is a natural extension of that an FC-group, that is, a group in which every
element has a finite number of conjugates. It is known that if G is an FC-group then the central factor G/Z(G) is periodic.
This result does not hold for CC-groups and in this paper we study CC-groups G in which the central factor G/Z(G) is periodic,
a finiteness condition which has a deep influence on the structure of the group G. In particular, we characterize those CC-groups
as above that are FC-groups by imposing some additional conditions on their structure.
This research has been supported by DGICYT (Spain) PS88-0085 相似文献
20.
We present a new operation to be performed on elements in a Garside group, called cyclic sliding, which is introduced to replace
the well known cycling and decycling operations. Cyclic sliding appears to be a more natural choice, simplifying the algorithms
concerning conjugacy in Garside groups and having nicer theoretical properties. We show, in particular, that if a super summit
element has conjugates which are rigid (that is, which have a certain particularly simple structure), then the optimal way of obtaining such a rigid conjugate through
conjugation by positive elements is given by iterated cyclic sliding. 相似文献