共查询到20条相似文献,搜索用时 15 毫秒
1.
令t(G)为有限阿贝尔群G的单因子个数.本文得到了∑|G|≤xt(G)带有更好余项的渐近公式. 相似文献
2.
Wenguang Zhai 《数学学报(英文版)》2000,16(4):549-554
Let t(G) be the number of unitary factors of finite abelian group G. In this paper we prove T(x)=∑
|G|≤x
t(G) = main terms for any exponent pair (κ1/2 + 2κ), which improves on the exponent 9/25 obtained by Xiaodong Cao and the author.
Received December 8, 1998, Revised April 27, 1998, Accepted June 12, 1998 相似文献
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A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design
approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find a general
lower bound on the size of a unitary t-design in U(d), for any d and t. We also introduce the notion of a unitary code—a subset of U(d) in which the trace inner product of any pair of matrices is restricted to only a small number of distinct absolute values—and
give an upper bound for the size of a code with s inner product values in U(d), for any d and s. These bounds can be strengthened when the particular inner product values that occur in the code or design are known. Finally,
we describe some constructions of designs: we give an upper bound on the size of the smallest weighted unitary t-design in U(d), and we catalogue some t-designs that arise from finite groups.
相似文献
5.
Homology Stability for Unitary Groups II 总被引:1,自引:0,他引:1
B. Mirzaii 《K-Theory》2005,36(3-4):305-326
In this paper, the homology stability problem for hyperbolic unitary groups over a local ring with an infinite residue field
is studied. We obtain a much better range of homology stability compared to the results existing in the literature. An application
of our results is given. 相似文献
6.
设Fq2(n)是 Fq2上的 n 维行向量空间, Un( Fq2)是 Fq2上的 n 阶酉群. 设M(m, r; n)是Un(Fq2}作用下的一个子空间轨道, L(m, r; n)是 M (m, r; n)中子空间的和生成的集合.该文讨论了各个轨道生成的集合L(m, r; n)之间的包含关系, 给出了一个子空间是属于给定的由M(m, r; n)生成的集合L(m, r, n)中的一个元素的条件, 以及L}(m, r; n)做成几何格的条件. 相似文献
7.
In this article, we generalize the class of meromorphic functions with bounded boundary rotation and related classes. Characterizations and some properties of these classes of functions are given. 相似文献
8.
C. Bekh-Ochir 《代数通讯》2013,41(8):2697-2706
We describe the T-ideal of identities and the T-space of central polynomials for the unitary finite dimensional Grassmann algebra over a finite field. 相似文献
9.
In the present paper we define an antilinear anti-involution ωof the q-Virasoro (Virq for short), and an Hermitian contravariant form of a Virq-module. For the irreducible module Vq(a,b) over Virq we give a necessary and sufficient condition for Vq(a,b) having a non-degenerate Hermitian contravariant form, and a necessary and sufficient condition for the Hermitian form being unitary. 相似文献
10.
《代数通讯》2013,41(5):2381-2401
Abstract Let 𝒪 be a discrete valuation ring whose residue field 𝒪/𝔭 is finite and has odd characteristic. Let l be a positive integer. Set R = 𝒪/𝔭 l and let R = R[θ] be the ring obtained by adjoining to R a square root of a non-square unit. Consider the involution σ of R that fixes R elementwise and sends θ to ? θ. Let V be a free R-module of rank n > 0 endowed with a non-degenerate hermitian form ( , ) relative to σ. Let U n (R) be the subgroup of GL(V) that preserves ( , ). Let SU n (R) be the subgroup of all g ∈ U n (R) whose determinant is equal to one. Let Ψ be the Weil character of U n (R). All irreducible constituents of Ψ are determined. An explicit character formula is given for each of them. In particular, all character degrees are computed. For n > 2 the corresponding results are also obtained for the restriction of Ψ to SU n (R). 相似文献
11.
Eliana Francot 《Journal of Geometry》2001,70(1-2):59-65
In this paper the class of polarities in non commutative twisted field planes, defined in a paper of Biliotti, Jha and Johnson
([4]), is investigated. It is proved that these polarities are unitary and that the associated unitals have a collineation group
that fixes a point and is transitive on the remaining ones.
Received 9 October 1999; revised 8 January 2000. 相似文献
12.
Let K be a nonabsolute field of characteristic p ≠ 2, G a locally finite group and KG its group algebra. Let ?: KG → KG denote the K-linear extension of an involution ? defined on G. In this article, we prove that if the subgroup 𝒰?(KG), i.e., the ?-unitary units of KG, satisfies a group identity, then KG satisfies a polynomial identity. Moreover, in case the prime radical of KG is nilpotent, we characterize the groups G for which 𝒰?(KG) satisfies a group identity. 相似文献
13.
James E. Tener 《Journal of Mathematical Analysis and Applications》2008,341(1):640-648
We present a necessary and sufficient condition for a 3×3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm whereby an arbitrary 3×3 matrix can be tested. This test generalizes to a necessary and sufficient condition that applies to almost every n×n matrix. The test is constructive in that it explicitly exhibits the unitary equivalence to a complex symmetric matrix. 相似文献
14.
Trae Holcomb 《代数通讯》2013,41(7):2496-2508
This article completes a previous investigation of balanced and unitary numerical semigroups. The main result establishes the equivalence of unitary numerical semigroups and perfect 2 × 2 bricks. 相似文献
15.
Ding Xuanhao 《东北数学》1997,(2)
OnUnitaryEquivalenceofAnalyticToeplitzOperatorsDingXuanhao(丁宣浩)(DaxianTeacher'sColege,Daxian,Sichuan,635000)AbstractInthispap... 相似文献
16.
高有 《数学物理学报(A辑)》2005,25(4):564-568
设K=F_(q^2),其特征为p, q=p^α,K有对合自同构ω:a→a^q. G是一个p 群,其阶为p^β, 群代数R=KG为一局部环. K的2阶自同构ω可延拓为R的一个2阶自同构,记为ω',为方便,对任意a∈R, 记ω‘(a)为~a. R上2n级酉群定义为U_(2n)R={A∈GL_(2n)R|A(0,I^n,I^n,0)~A^t=(0,I^n,I^n,0)} 该文计算了U_(2n)R的阶. 相似文献
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Yong He & Chun-Ping Zhong 《数学研究》2016,49(1):13-22
In this paper,we prove that a unitary invariant strongly pseudoconvex complex
Finsler metric is a complex Landsberg metric if and if only if it comes from a
unitary invariant Hermitian metric. This implies that there does not exist unitary invariant
complex Landsberg metric unless it comes from a unitary invariant Hermitian
metric. 相似文献