共查询到10条相似文献,搜索用时 93 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.
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
9.
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
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