共查询到20条相似文献,搜索用时 62 毫秒
1.
A characterization is given of the class of edge-transitive Cayley graphs of Frobenius groups
\mathbbZpd:\mathbbZq\mathbb{Z}_{p^{d}}{:}\mathbb{Z}_{q} with p,q odd prime, of valency coprime to p. This characterization is then used to study an isomorphism problem regarding Cayley graphs, and to construct new families
of half-arc-transitive graphs. 相似文献
2.
Cristina Fernández-Córdoba Jaume Pujol Mercè Villanueva 《Designs, Codes and Cryptography》2010,56(1):43-59
A code C{{\mathcal C}} is
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive codes under an extended Gray map are called
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes. In this paper, the invariants for
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the rank and dimension of the kernel, are studied. Specifically, given the algebraic parameters of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the possible values of these two invariants, giving lower and upper bounds, are established. For each possible
rank r between these bounds, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code for each possible pair (r, k) is given. 相似文献
3.
Gábor Somlai 《Journal of Algebraic Combinatorics》2011,34(3):323-335
For every prime p>2 we exhibit a Cayley graph on
\mathbbZp2p+3\mathbb{Z}_{p}^{2p+3} which is not a CI-graph. This proves that an elementary abelian p-group of rank greater than or equal to 2p+3 is not a CI-group. The proof is elementary and uses only multivariate polynomials and basic tools of linear algebra. Moreover,
we apply our technique to give a uniform explanation for the recent works of Muzychuk and Spiga concerning the problem. 相似文献
4.
Hae-Sang Sun 《Mathematische Annalen》2010,348(4):909-927
We consider a cuspidal class number, which is the order of a subgroup of the full cuspidal divisor class group of X
1(Np
n
) with
p\nmid N{p\nmid N} and n ≥ 1. By studying the second generalized Bernoulli numbers, we obtain results similar to ones (Ferrero and Washington in Ann
Math (2) 109(2):377–395, 1979; Washington in Invent Math 49:87–97, 1978) about the relative class numbers of cyclotomic
\mathbbZp{\mathbb{Z}_p}-extension of an abelian number field. 相似文献
5.
Yong-Kum Cho Sunggeum Hong Joonil Kim Chan Woo Yang 《Integral Equations and Operator Theory》2009,65(4):485-528
Given
W ì \mathbbZ+3\Omega \subset {\mathbb{Z}}_{+}^{3}, we discuss a necessary and sufficient condition that the triple Hilbert transform associated with any polynomial of the
form ($t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m$t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m) is bounded in
Lp(\mathbbR4)L^p({\mathbb{R}}^4). 相似文献
6.
A group G is said to be capable if it is isomorphic to the central factor group H/Z(H) for some group H. Let G be a nonabelian group of order p
2
q for distinct primes p and q. In this paper, we compute the nonabelian tensor square of the group G. It is also shown that G is capable if and only if either Z(G) = 1 or p < q and
Gab=\mathbbZp×\mathbbZp{G^{\rm ab}=\mathbb{Z}_{p}\times\mathbb{Z}_{p}} . 相似文献
7.
Let
\mathbbZpm \mathbb{Z}_{p^m } be the ring of integers modulo p
m
, where p is a prime and m ⩾ 1. The general linear group GL
n
(
\mathbbZpm \mathbb{Z}_{p^m } ) acts naturally on the polynomial algebra A
n
:=
\mathbbZpm \mathbb{Z}_{p^m } [x
1, …, x
n
]. Denote by
AnGL2 (\mathbbZpm ) A_n^{GL_2 (\mathbb{Z}_{p^m } )} the corresponding ring of invariants. The purpose of the present paper is to calculate this invariant ring. Our results also
generalize the classical Dickson’s theorem. 相似文献
8.
Bent and almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are studied in this paper. By calculating certain exponential sum and using a technique due to Hou (Finite Fields Appl 10:566–582,
2004), we obtain a degree bound for quasi-bent functions, and prove that almost-bent functions on
\mathbbZp2{\mathbb{Z}_p^2} are equivalent to a degenerate quadratic form. From the viewpoint of relative difference sets, we also characterize bent
functions on
\mathbbZp2{\mathbb{Z}_p^2} in two classes of M{\mathcal{M}} ’s and PS{\mathcal{PS}} ’s, and show that the graph set corresponding to a bent function on
\mathbbZp2{\mathbb{Z}_p^2} can be written as the sum of a graph set of M{\mathcal{M}} ’s type bent function and another group ring element. By using our characterization and some technique of permutation polynomial,
we obtain the result: a bent function must be of M{\mathcal{M}} ’s type if its corresponding set contains more than (p − 3)/2 flats. A problem proposed by Ma and Pott (J Algebra 175:505–525, 1995) is therefore partially answered. 相似文献
9.
The motivation for this paper comes from the Halperin–Carlsson conjecture for (real) moment-angle complexes. We first give
an algebraic combinatorics formula for the M?bius transform of an abstract simplicial complex K on [m]={1,…,m} in terms of the Betti numbers of the Stanley–Reisner face ring k(K) of K over a field k. We then employ a way of compressing K to provide the lower bound on the sum of those Betti numbers using our formula. Next we consider a class of generalized moment-angle
complexes
ZK(\mathbb D, \mathbb S)\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})}, including the moment-angle complex ZK\mathcal{Z}_{K} and the real moment-angle complex
\mathbbRZK\mathbb{R}\mathcal {Z}_{K} as special examples. We show that
H*(ZK(\mathbb D, \mathbb S);k)H^{*}(\mathcal{Z}_{K}^{(\underline{\mathbb{ D}}, \underline{\mathbb{ S}})};\mathbf{k}) has the same graded k-module structure as Tor
k[v](k(K),k). Finally we show that the Halperin–Carlsson conjecture holds for ZK\mathcal{Z}_{K} (resp.
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}) under the restriction of the natural T
m
-action on ZK\mathcal{Z}_{K} (resp. (ℤ2)
m
-action on
\mathbb RZK\mathbb{ R}\mathcal{Z}_{K}). 相似文献
10.
O. Yu. Dashkova 《Ukrainian Mathematical Journal》2012,63(9):1379-1389
We study a
\mathbbZG \mathbb{Z}G -module A such that
\mathbbZ \mathbb{Z} is the ring of integer numbers, the group G has an infinite sectional p-rank (or an infinite 0-rank), C
G
(A) = 1, A is not a minimax
\mathbbZ \mathbb{Z} -module, and, for any proper subgroup H of infinite sectional p-rank (or infinite 0-rank, respectively), the quotient module A/C
A
(H) is a minimax
\mathbbZ \mathbb{Z} -module. It is shown that if the group G is locally soluble, then it is soluble. Some properties of soluble groups of this kind are discussed. 相似文献
11.
Birgit Jacob 《Integral Equations and Operator Theory》2003,46(2):189-214
In this paper a system is considered as a (possibly unbounded) linear operator from l2\mathbb(Z)m \ell_{2}\mathbb{(Z)}^{m} to l2\mathbb(Z)p \ell_{2}\mathbb{(Z)}^{p} . Georgiou and Smith [6] noted that there are intrinsic difficulties in using l2\mathbb(Z) \ell_{2}\mathbb{(Z)} as underlying signal space, since even a simple causal convolution system is not closed and an extended definition of the system is not causal. We discuss these difficulties and we develop necessary and sufficient conditions for notions such as causality, closability and causal closability. 相似文献
12.
We describe the dynamics of an arbitrary affine dynamical system on a local field by exhibiting all its minimal subsystems.
In the special case of the field
\mathbbQp{\mathbb{Q}_p} of p-adic numbers, for any non-trivial affine dynamical system, we prove that the field
\mathbbQp{\mathbb{Q}_p} is decomposed into a countable number of invariant balls or spheres each of which consists of a finite number of minimal
subsets. Consequently, we give a complete classification of topological conjugacy for non-trivial affine dynamics on
\mathbbQp{\mathbb{Q}_p} . For each given prime p, there is a finite number of conjugacy classes. 相似文献
13.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
Let ${\mathfrak{g}}Let
\mathfrakg{\mathfrak{g}} be a finite dimensional simple Lie algebra over an algebraically closed field
\mathbbK\mathbb{K} of characteristic 0. Let
\mathfrakg\mathbbZ{\mathfrak{g}}_{{\mathbb{Z}}} be a Chevalley ℤ-form of
\mathfrakg{\mathfrak{g}} and
\mathfrakg\Bbbk=\mathfrakg\mathbbZ?\mathbbZ\Bbbk{\mathfrak{g}}_{\Bbbk}={\mathfrak{g}}_{{\mathbb{Z}}}\otimes _{{\mathbb{Z}}}\Bbbk, where
\Bbbk\Bbbk is the algebraic closure of
\mathbbFp{\mathbb{F}}_{p}. Let
G\BbbkG_{\Bbbk} be a simple, simply connected algebraic
\Bbbk\Bbbk-group with
\operatornameLie(G\Bbbk)=\mathfrakg\Bbbk\operatorname{Lie}(G_{\Bbbk})={\mathfrak{g}}_{\Bbbk}. In this paper, we apply recent results of Rudolf Tange on the fraction field of the centre of the universal enveloping algebra
U(\mathfrakg\Bbbk)U({\mathfrak{g}}_{\Bbbk}) to show that if the Gelfand–Kirillov conjecture (from 1966) holds for
\mathfrakg{\mathfrak{g}}, then for all p≫0 the field of rational functions
\Bbbk (\mathfrakg\Bbbk)\Bbbk ({\mathfrak{g}}_{\Bbbk}) is purely transcendental over its subfield
\Bbbk(\mathfrakg\Bbbk)G\Bbbk\Bbbk({\mathfrak{g}}_{\Bbbk})^{G_{\Bbbk}}. Very recently, it was proved by Colliot-Thélène, Kunyavskiĭ, Popov, and Reichstein that the field of rational functions
\mathbbK(\mathfrakg){\mathbb{K}}({\mathfrak{g}}) is not purely transcendental over its subfield
\mathbbK(\mathfrakg)\mathfrakg{\mathbb{K}}({\mathfrak{g}})^{\mathfrak{g}} if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4. We prove a modular version of this result (valid for p≫0) and use it to show that, in characteristic 0, the Gelfand–Kirillov conjecture fails for the simple Lie algebras of the
above types. In other words, if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4, then the Lie field of
\mathfrakg{\mathfrak{g}} is more complicated than expected. 相似文献
14.
Swarnendu Datta 《Transformation Groups》2010,15(1):72-91
Let G be a commutative, unipotent, perfect, connected group scheme over an algebraically closed field of characteristic p > 0 and let E be a biextension of G × G by the discrete group
\mathbbQp/\mathbbZp\mathbb{Q}_{p}/\mathbb{Z}_{p}. When E is skew-symmetric, V. Drinfeld defined a certain metric group A associated to E (when G is the perfectization of the additive group
\mathbbGa\mathbb{G}_{a}, it is easy to compute this metric group, cf. Appendix A). In this paper we prove a conjecture due to Drinfeld about the
class of the metric group A in the Witt group (cf. Appendix B). 相似文献
15.
Takuro Fukunaga 《Graphs and Combinatorics》2011,27(5):647-659
An undirected graph G = (V, E) is called
\mathbbZ3{\mathbb{Z}_3}-connected if for all
b: V ? \mathbbZ3{b: V \rightarrow \mathbb{Z}_3} with ?v ? Vb(v)=0{\sum_{v \in V}b(v)=0}, an orientation D = (V, A) of G has a
\mathbbZ3{\mathbb{Z}_3}-valued nowhere-zero flow
f: A? \mathbbZ3-{0}{f: A\rightarrow \mathbb{Z}_3-\{0\}} such that ?e ? d+(v)f(e)-?e ? d-(v)f(e)=b(v){\sum_{e \in \delta^+(v)}f(e)-\sum_{e \in \delta^-(v)}f(e)=b(v)} for all v ? V{v \in V}. We show that all 4-edge-connected HHD-free graphs are
\mathbbZ3{\mathbb{Z}_3}-connected. This extends the result due to Lai (Graphs Comb 16:165–176, 2000), which proves the
\mathbbZ3{\mathbb{Z}_3}-connectivity for 4-edge-connected chordal graphs. 相似文献
16.
Yurii G. Leonov 《Journal of Mathematical Sciences》2011,179(2):290-299
A wreath product of the type
\mathbbZ2 \wr G {\mathbb{Z}_2} \wr G is considered for any finite 2-group G. The monomorphism of such a group in the well-known Kaloujnine group P
2,m
is studied for a suitable natural m. 相似文献
17.
完整地确定了换位子群是不可分Abel群的有限秩可除幂零群的结构,证明了下面的定理.设G是有限秩的可除幂零群,则G的换位子群是不可分Abel群当且仅当G'=Q或Q_p/Z且G可以分解为G=S×D,其中当G'=Q时,■当G'=Q_p/Z时,S有中心积分解S=S_1*S_2*…*S_r,并且可以将S形式化地写成■其中■,式中s,t都是非负整数,Q是有理数加群,π_κ(k=1,2,…,t)是某些素数的集合,满足π_1■Cπ_2■…■π_t,Q_π_k={m/n|(m,n)=1,m∈Z,n为正的π_k-数}.进一步地,当G'=Q时,(r;s;π_1,π_2,…,π_t)是群G的同构不变量;当G'=Q_p/Z时,(p,r;s;π_1,π_2,…,πt)是群G的同构不变量.即若群H也是有限秩的可除幂零群,它的换位子群是不可分Abel群,那么G同构于H的充分必要条件是它们有相同的不变量. 相似文献
18.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
19.
Yu. S. Kolomoitsev 《Journal of Mathematical Sciences》2010,165(4):463-472
Let B be a set of integers with certain arithmetic properties. We obtain estimates of the best approximation of functions in the
space L
p
, 0 < p <1, by trigonometric polynomials that are constructed by the system
{eikx}k ? \mathbbZ\B \{e^{ikx}\}_{k\in \mathbb{Z}\backslash B} . Bibliography: 13 titles. 相似文献
20.
A Toeplitz operator TfT_\phi with symbol f\phi in
L¥(\mathbbD)L^{\infty}({\mathbb{D}}) on the Bergman space
A2(\mathbbD)A^{2}({\mathbb{D}}), where
\mathbbD\mathbb{D} denotes the open unit disc, is radial if f(z) = f(|z|)\phi(z) = \phi(|z|) a.e. on
\mathbbD\mathbb{D}. In this paper, we consider the numerical ranges of such operators. It is shown that all finite line segments, convex hulls
of analytic images of
\mathbbD\mathbb{D} and closed convex polygonal regions in the plane are the numerical ranges of radial Toeplitz operators. On the other hand,
Toeplitz operators TfT_\phi with f\phi harmonic on
\mathbbD\mathbb{D} and continuous on
[`(\mathbbD)]{\overline{\mathbb{D}}} and radial Toeplitz operators are convexoid, but certain compact quasinilpotent Toeplitz operators are not. 相似文献