共查询到20条相似文献,搜索用时 31 毫秒
1.
O. Yu. Dashkova 《Journal of Mathematical Sciences》2010,164(2):228-233
The author studies a D
G-module A such that D is a Dedekind domain, A/C
A
(G) is not an Artinian D-module, C
A
(G) = 1, G is a soluble group, and the system of all subgroups H ≤ G for which the quotient modules A/C
A
(H) are not Artinian D-modules satisfies the minimum condition. The structure of G is described. 相似文献
2.
Qi Yu Sun 《数学学报(英文版)》2001,17(1):1-14
Let A be a matrix with the absolute values of all eigenvalues strictly larger than one, and let Z
0 be a subset of Z such than n∈Z
0 implies n + 1 ∈Z
0. Denote the space of all compactly supported distributions by D′, and the usual convolution between two compactly supported distributions f and g by f*g. For any bounded sequence G
n
and H
n
, n∈Z
0, in D′, define the corresponding nonstationary nonhomogeneous refinement equation
Φ
n
=H
n
*Φ
n+1
(A·)+G
n
for all n∈Z
0
where Φ
n
, n∈Z
0, is in a bounded set of D′. The nonstationary nonhomogeneous refinement equation (*) arises in the construction of wavelets on bounded domain, multiwavelets,
and of biorthogonal wavelets on nonuniform meshes. In this paper, we study the existence problem of compactly supported distributional
solutions Φ
n
, n∈Z
0, of the equation (*). In fact, we reduce the existence problem to finding a bounded solution of the linear equations
for all n∈Z
0
where the matrices S
n
and the vectors , n∈Z
0, can be constructed explicitly from H
n
and G
n
respectively. The results above are still new even for stationary nonhomogeneous refinement equations.
Received December 30, 1999, Accepted June 15, 2000 相似文献
3.
Let G be a finite group with derived subgroup of rank r. We prove that |G: Z
2(G)| ≤ |G′|2r
. Motivated by the results of I. M. Isaacs in [5] we show that if G is capable then |G: Z(G)| ≤ |G′|4r
. This answers a question of L. Pyber. We prove that if G is a capable p-group then the rank of G/Z(G) is bounded above in terms of the rank of G′. 相似文献
4.
5.
Let S be a fixed finite symmetric subset of SL
d
(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of π
q
(G) with respect to the generating set π
q
(S) form a family of expanders, where π
q
is the projection map Z→Z/q
Z. 相似文献
6.
Frank Jonas 《manuscripta mathematica》1990,67(1):35-39
Zusammenfassung LetD:G→GL(n,C) be an irreducible linear representation of a finite groupG with the characterX. IfD is realizible in Q(ξ
m
) and Q(ξ
m′
) we give a condition for then realizability ofD in Q(ξ(m′)). If the degreen is a prime ≠ 2, we show thatD realizible in Q(ξ
f
), wheref is the conductor of the abelian extensionQ(X)/Q. 相似文献
7.
Letk be any field andG a finite group. Given a cohomology class α∈H
2(G,k
*), whereG acts trivially onk
*, one constructs the twisted group algebrak
αG. Unlike the group algebrakG, the twisted group algebra may be a division algebra (e.g. symbol algebras, whereG⋞Z
n×Zn). This paper has two main results: First we prove that ifD=k
α
G is a division algebra central overk (equivalentyD has a projectivek-basis) thenG is nilpotent andG’ the commutator subgroup ofG, is cyclic. Next we show that unless char(k)=0 and
, the division algebraD=k
α
G is a product of cyclic algebras. Furthermore, ifD
p is ap-primary factor ofD, thenD
p is a product of cyclic algebras where all but possibly one are symbol algebras. If char(k)=0 and
, the same result holds forD
p, p odd. Ifp=2 we show thatD
2 is a product of quaternion algebras with (possibly) a crossed product algebra (L/k,β), Gal(L/k)⋞Z
2×Z2n. 相似文献
8.
F. E. A. Johnson 《代数通讯》2013,41(5):2034-2047
Let G be a finite group with integral group ring Λ =Z[G]. The syzygies Ωr(Z) are the stable classes of the intermediate modules in a free Λ-resolution of the trivial module. They are of significance in the cohomology theory of G via the “co-represention theorem” Hr(G, N) = Hom𝒟er(Ωr(Z), N). We describe the Ωr(Z) explicitly for the dihedral groups D4n+2, so allowing the construction of free resolutions whose differentials are diagonal matrices over Λ. 相似文献
9.
Let (G, χ, x) be a triple consisting of a finitely presented groupG, epimorphism χ:G →Z, and distinguished elementx ∈G such that χ(x)=1. Given a finite symmetric groupS
r, we construct a finite directed graph Γ that describes the set Φ
r
of representations π: Ker χ →S
r as well as the mapping σ
x
:Φ
r
→Φ
r
defined by (σ
x
ϱ)(a) = ϱ(x
−1
ax) for alla ∈ Ker χ. The pair (Φ
r
,σ
x
has the structure of a shift of finite type, a well-known type of compact 0-dimensional dynamical system. We discuss basic
properties and applications of therepresentation shift (Φ
r
,σ
x
), including applications to knot theory. 相似文献
10.
Let G be a finite group and U(Z(Z
G)) be the group of units of the center Z(Z
G) of the integral group ring Z
G (the central unit group of the ring Z
G). The purpose of the present work is to study the ranks r
n
of groups U(Z(ZAn)), i.e., of central unit groups of integral group rings of alternating groups A
n
. We shall find all values n for r
n
= 1 and propose an approach on how to describe the groups U(Z(ZAn)) in these cases, and we will present some results of calculations of r
n
for n ≤ 600. 相似文献
11.
Edward A. Bertram 《Israel Journal of Mathematics》1984,47(4):335-344
In 1955 R. Brauer and K. A. Fowler showed that ifG is a group of even order >2, and the order |Z(G)| of the center ofG is odd, then there exists a strongly real) elementx∈G−Z whose centralizer satisfies|C
G(x)|>|G|1/3. In Theorem 1 we show that every non-abeliansolvable groupG contains an elementx∈G−Z such that|C
G(x)|>[G:G′∩Z]1/2 (and thus|C
G(x)|>|G|1/3). We also note that if non-abelianG is either metabelian, nilpotent or (more generally) supersolvable, or anA-group, or any Frobenius group, then|C
G(x)|>|G|1/2 for somex∈G−Z. In Theorem 2 we prove that every non-abelian groupG of orderp
mqn (p, q primes) contains a proper centralizer of order >|G|1/2. Finally, in Theorem 3 we show that theaverage
|C(x)|, x∈G, is ≧c|G|
1/3 for metabelian groups, wherec is constant and the exponent 1/3 is best possible. 相似文献
12.
LetK be the kernel of an epimorphismG→ℤ, whereG is a finitely presented group. IfK has infinitely many subgroups of index 2,3 or 4, then it has uncountably many. Moreover, ifK is the commutator subgroup of a classical knot groupG, then any homomorphism fromK onto the symmetric groupS
2 (resp. ℤ3) lifts to a homomorphism ontoS
3 (resp. alternating groupA
4).
Both authors partially supported by NSF grants DMS-0071004 and DMS-0304971. 相似文献
13.
Abraham Neyman 《Israel Journal of Mathematics》1981,40(1):54-64
The following conditions on a zonoidZ, i.e., a range of a non-atomic vector measure, are equivalent: (i) the extreme set containing 0 in its relative interior
is a parallelepiped; (ii) the zonoidZ determines them-range of any non-atomic vector measure with rangeZ, where them-range of a vector measure μ is the set ofm-tuples (μ(S
1), …, μ(S
m), whereS
1, …S
m
are disjoint measurable sets and (iii) there is avector measure space (X, Σ, μ) such that any finite factorization ofZ, Z =ΣZ
i
, in the class of zonoids could be achieved by decomposing (X, Σ). In the case of ranges of non-atomic probability measures (i) is automatically satisfied, so (ii) and (iii) hold.
Partially supported by NSF grant MCS-79-06634 相似文献
14.
We prove that the symplectic group
Sp(2n,\mathbbZ){Sp(2n,\mathbb{Z})} and the mapping class group Mod
S
of a compact surface S satisfy the R
∞ property. We also show that B
n
(S), the full braid group on n-strings of a surface S, satisfies the R
∞ property in the cases where S is either the compact disk D, or the sphere S
2. This means that for any automorphism f{\phi} of G, where G is one of the above groups, the number of twisted f{\phi}-conjugacy classes is infinite. 相似文献
15.
Adam Harris 《Journal of Geometric Analysis》1995,5(4):533-550
Let ƒ:M →D ⊑C
n
be a holomorphic family of compact, complex surfaces, which is locally trivial onD∖Z, for an analytic subsetZ. Conditions are found under which ƒ extends trivially toD, if the fibers of ƒ|D∖Z are either Hirzebruch surfaces (projective bundles overP
1), Hopf surfaces (elliptic bundles overP
1), hyperelliptic bundles, or any compact complex surface having one of these as minimal model under blowing-down. The results
of this paper are motivated by the existence of non-Hausdorff moduli spaces in the deformation of complex structure for certain
complex manifolds. 相似文献
16.
Every elementr of reduced trace 0 in a simple finite dimensional algebraR is a sum of at most 2 commutators. IfR innot a division ring thenr is a commutator, unlessr is a scalar (in which case char(R)≠0). The method of proof provides a generic division algebra of transcendence degreen
2−1. 相似文献
17.
Pierre Liardet 《Israel Journal of Mathematics》1981,39(4):303-325
LetS
φ be the skew product transformation(x, g)↦(Sx, gφ(x)) defined on Ω×G, where Ω is a compact metric space,G a compact metric group with its Haar measureh. IfS is a μ-continuous transformation where μ is a Borel measure on Ω, ergodic with respect toS, we study the setE
0 of μ-continuous applications φ:Ω→G such that μ⩀h is ergodic (with respect toS
φ). For example,E
0 is residual in the group of μ-continuous applications from Ω toG with the uniform convergence topology. We also study the weakly mixing case. Some arithmetic applications are given. 相似文献
18.
Britta Späth 《Mathematische Zeitschrift》2009,261(3):571-595
Let G be a simply-connected simple algebraic group over an algebraically closed field of characteristic p with a Frobenius map F : G → G and G := G
F
, such that the root system is of exceptional type or G is a Suzuki group or Steinberg’s triality group. We show that all irreducible characters of C
G
(S), the centraliser of S in G, extend to their inertia group in N
G
(S), where S is any F-stable Sylow torus of (G, F). Together with the work in [16] this implies that the McKay conjecture is true for G and odd primes ℓ different from the defining characteristic. Moreover it shows important properties of the associated simple
groups, which are relevant for the proof that the associated simple groups are good in the sense of Isaacs, Malle and Navarro,
as defined in [14].
This research has been supported by the DFG-grant “Die Alperin-McKay-Vermutung für endliche Gruppen” and an Oberwolfach Leibniz
fellowship. 相似文献
19.
We prove that for every abelian groupG and every compactumX with dim
G
X ≤n ≥ 2 there is aG-acyclic resolutionr:Z→X from a compactumZ with dim
G
Z≤n and dimZ≤n+1 ontoX. 相似文献
20.
. Let d(D) (resp., d(G)) denote the diameter and r(D) (resp., r(G)) the radius of a digraph D (resp., graph G). Let G×H denote the cartesian product of two graphs G and H. An orientation D of G is said to be (r, d)-invariant if r(D)=r(G) and d(D)=d(G). Let {T
i
}, i=1,…,n, where n≥2, be a family of trees. In this paper, we show that the graph ∏
i
=1
n
T
i
admits an (r, d)-invariant orientation provided that d(T
1)≥d(T
2)≥4 for n=2, and d(T
1)≥5 and d(T
2)≥4 for n≥3.
Received: July 30, 1997 Final version received: April 20, 1998 相似文献