共查询到20条相似文献,搜索用时 15 毫秒
1.
Hans TRIEBEL 《数学学报(英文版)》2008,24(4):539-554
A space Apq^s (R^n) with A : B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp(Г), where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D(R^n/Г) is dense in it. Related dichotomy numbers are introduced and calculated. 相似文献
2.
V. E. Kislyakov 《Algebra and Logic》1998,37(6):363-370
We study a group G containing an element g such that CG(g)∩gG is finite. The nonoriented graph Γ is defined as follows. The vertex set of Γ is the conjugacy class gG. Vertices x and y of the graph G are bridged by an edge iff x≠y and xy=yx. Let Γ0 be some connected component of G. On a condition that any two vertices of Γ0 generate a nilpotent group, it is proved that a subgroup generated by the vertex set of Γ0 is locally nilpotent.
Supported by the RF State Committee of Higher Education.
Translated fromAlgebra i Logika, Vol. 37, No. 6, pp. 637–650, November–December, 1998. 相似文献
3.
We define the notion of admissible pair for an algebra A, consisting on a couple (Γ, R), where Γ is a quiver and R a unital, splitted and factorizable representation of Γ, and prove that the set of admissible pairs for A is in one to one correspondence with the points of the variety of twisting maps TAn:=T(Kn,A)\mathcal{T}_A^n:=\mathcal{T}(K^n,A). We describe all these representations in the case A = K
m
. 相似文献
4.
Barak Weiss 《Israel Journal of Mathematics》2006,152(1):221-227
The author proves a conjecture of the author: IfG is a semisimple real algebraic defined over ℚ, Γ is an arithmetic subgroup (with respect to the given ℚ-structure) andA is a diagonalizable subgroup admitting a divergent trajectory inG/Γ, then dimA≤ rankℚ
G. 相似文献
5.
V. E. Kislyakov 《Algebra and Logic》1996,35(5):305-309
We study the problem as to which is the cardinality of connected components of the graph Γα, defined as follows. Let G be a group and a an element of G. The vertex set V(Γα) of the graph is the conjugacy class of elements,Cl
G(a), and two vertices x and y of the graph Γα are bridged by an edge iff x=y. If the intersectionC
G(a)∩Cl
G(a) is finite, Γα is locally finite. We prove that connected components of the locally finite graph Γα are finite in some classes of groups.
Supported by RFFR grant No. 94-01-01084.
Translated fromAlgebra i Logika, Vol. 35, No. 5, pp. 543–551, September–October, 1996. 相似文献
6.
7.
Let Out(F
n
) denote the outer automorphism group of the free group F
n
with n>3. We prove that for any finite index subgroup Γ<Out(F
n
), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(F
n
). We prove that Γ is co-Hopfian: every injective homomorphism Γ→Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(F
n
)) is isomorphic to Out(F
n
). 相似文献
8.
Brian Curtin 《Graphs and Combinatorics》1999,15(2):143-158
Let Γ=(X,E) denote a bipartite distance-regular graph with diameter D≥4, and fix a vertex x of Γ. The Terwilliger algebra
T=T(x) is the subalgebra of Mat
X(C) generated by A, E
*
0, E
*
1,…,E
*
D, where A denotes the adjacency matrix for Γ and E
*
i denotes the projection onto the i
TH subconstituent of Γ with respect to x. An irreducible T-module W is said to be thin whenever dimE
*
i
W≤1 for 0≤i≤Di. The endpoint of W is min{i|E
*
i
W≠0}.
We determine the structure of the (unique) irreducible T-module of endpoint 0 in terms of the intersection numbers of Γ. We show that up to isomorphism there is a unique irreducible
T-module of endpoint 1 and it is thin. We determine its structure in terms of the intersection numbers of Γ. We determine the
structure of each thin irreducible T-module W of endpoint 2 in terms of the intersection numbers of Γ and an additional real parameter ψ=ψ(W), which we refer to as the type of W.
We now assume each irreducible T-module of endpoint 2 is thin and obtain the following two-fold result. First, we show that the intersection numbers of Γ
are determined by the diameter D of Γ and the set of ordered pairs
where Φ2 denotes the set of distinct types of irreducible T-modules with endpoint 2, and where mult(ψ) denotes the multiplicity with which the module of type ψ appears in the standard
module. Secondly, we show that the set of ordered pairs {(ψ,mult(ψ)) |ψ∈Φ2} is determined by the intersection numbers k, b
2, b
3 of Γ and the spectrum of the graph , where
and where ∂ denotes the distance function in Γ. Combining the above two results, we conclude that if every irreducible T-module of endpoint 2 is thin, then the intersection numbers of Γ are determined by the diameter D of Γ, the intersection numbers k, b
2, b
3 of Γ, and the spectrum of Γ2
2.
Received: November 13, 1995 / Revised: March 31, 1997 相似文献
9.
Peter Abramenko 《Israel Journal of Mathematics》1994,87(1-3):203-223
LetG be a simple Chevalley group of rankn and Γ=G(
). Then the finiteness length of Γ shall be determined by studying the action of Γ on the Bruhat-Tits buildingX ofG
. This is always possible provided that certain subcomplexes of the links of simplices inX are spherical. As a consequence, one obtains that Γ is of typeF
n−1 but not of typeFP
n ifG is of typeA
n, Bn, Cn orD
n andq≥22n−1. 相似文献
10.
V. D. Mazurov 《Algebra and Logic》2006,45(2):117-123
Let G be a group. A subset X of G is called an A-subset if X consists of elements of order 3, X is invariant in G, and every
two non-commuting members of X generate a subgroup isomorphic to A4 or to A5. Let X be the A-subset of G. Define a non-oriented graph Γ(X) with vertex set X in which two vertices are adjacent iff they
generate a subgroup isomorphic to A4. Theorem 1 states the following. Let X be a non-empty A-subset of G. (1) Suppose that C is a connected component of Γ(X)
and H = 〈C〉. If H ∩ X does not contain a pair of elements generating a subgroup isomorphic to A5 then H contains a normal elementary Abelian 2-subgroup of index 3 and a subgroup of order 3 which coincides with its centralizer
in H. In the opposite case, H is isomorphic to the alternating group A(I) for some (possibly infinite) set I, |I| ≥ 5. (2)
The subgroup 〈XG〉 is a direct product of subgroups 〈C
α〉-generated by some connected components C
α of Γ(X). Theorem 2 asserts the following. Let G be a group and X⊆G be a non-empty G-invariant set of elements of order 5 such that every two non-commuting members of X generate a subgroup
isomorphic to A5. Then 〈XG〉 is a direct product of groups each of which either is isomorphic to A5 or is cyclic of order 5.
Supported by RFBR grant No. 05-01-00797; FP “Universities of Russia,” grant No. UR.04.01.028; RF Ministry of Education Developmental
Program for Scientific Potential of the Higher School of Learning, project No. 511; Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.
__________
Translated from Algebra i Logika, Vol. 45, No. 2, pp. 203–214, March–April, 2006. 相似文献
11.
Let Γ be a regular curve and Lp(Γ),1<p<+∞, be the class of all complex-valued functions f defined on Γ which are such that |f|p is integrable in sense of Lebesgue. In this work, we define the kth p-Faber polynomial Fk.p(z), the kth p-Faber principle part ≈Fk.p(1/z) for Γ, and defined the nth p-Faber-Laurent rational function Rn,p(f, z) and p-generalized modulus of continuity Ωp of a function f of Lp(Γ). We investigate some properties of Fk.p(z) and ≈Fk.p(1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ωp in the mean of functions of Lp(Γ) by the rational functions Rn.p(.,z). 相似文献
12.
Let F n be the free group of rank n, and let Aut+(F n ) be its special automorphism group. For an epimorphism π : F n → G of the free group F n onto a finite group G we call the standard congruence subgroup of Aut+(F n ) associated to G and π. In the case n = 2 we fully describe the abelianization of Γ+(G, π) for finite abelian groups G. Moreover, we show that if G is a finite non-perfect group, then Γ+(G, π) ≤ Aut+(F 2) has infinite abelianization. 相似文献
13.
A. Zaks 《Israel Journal of Mathematics》1968,6(4):359-362
A semi-primary hereditary ring Σ, with radicalM and residue ring Γ=Σ/M, is uniquely determined by Γ and a Γ-bimoduleA=M/M
2, whenever Σ admits a splitting Σ=Γ+A+M
2. 相似文献
14.
Simon M. Smith 《Journal of Algebraic Combinatorics》2010,31(1):131-141
A group G of permutations of a set Ω is primitive if it acts transitively on Ω, and the only G-invariant equivalence relations on Ω are the trivial and universal relations.
A digraph Γ is primitive if its automorphism group acts primitively on its vertex set, and is infinite if its vertex set is infinite. It has connectivity one if it is connected and there exists a vertex α of Γ, such that the induced digraph Γ∖{α} is not connected. If Γ has connectivity one, a lobe of Γ is a connected subgraph that is maximal subject to the condition that it does not have connectivity one. Primitive graphs
(and thus digraphs) with connectivity one are necessarily infinite. 相似文献
15.
16.
L. A. Gilch 《Journal of Mathematical Sciences》2009,156(1):173-186
Suppose we are given a homogeneous tree {ie173-01} of degree q ≥ 3, where at each vertex sits a lamp, which can be switched on or off. This structure can be described by the wreath product
(ℤ/2)≀Γ, where Γ = *
i=1qℤ/2 is the free product group of q factors ℤ/2. We consider a transient random walk on a Cayley graph of (ℤ/2) ≀Γ, for which we want to compute lower and upper
bounds for the rate of escape, that is, the speed at which the random walk flees to infinity.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 50, Functional
Analysis, 2007. 相似文献
17.
Christophe Breuil 《Israel Journal of Mathematics》2011,182(1):349-382
Let ρ be a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/ℚ
p
) over ̅F
p
. The modulo p Langlands correspondence for GL2(ℚ
p
) defined in [5], as realized in [9], can be reformulated as a quite simple recipee giving back the (φ, Γ)-module of the dual of ρ starting from the “Diamond diagram” associated to ρ. Let F be a finite unramified extension of ℚ
p
and ρ a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/F) over ̅F
p
. When one formally extends this recipee to the Diamond diagrams associated to ρ in [6], we show that one essentially finds the (φ, Γ)-module of the tensor induction from F to ℚ
p
of the dual of ρ. 相似文献
18.
Let F be a field, let A be a vector space over F, and let GL(F, A) be the group of all automorphisms of the space A. If H is a subgroup of GL(F, A), then we set aug dimF (H) = dimF (A(ωFH)), where ωFH is the augmentation ideal of the group ring FH. The number aug dimF (H) is called the augmentation dimension of the subgroup H. In the present paper, we study locally solvable linear groups with minimality condition for subgroups of infinite augmentation
dimension.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1476–1489, November, 2005. 相似文献
19.
Let A be an Artinian algebra and F an additive subbifunctor of Ext,(-, -) having enough projectives and injectives. We prove that the dualizing subvarieties of mod A closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod A and S a cotilting module over F = End(T). Then Horn(-, T) induces a duality between F-almost split sequences in ⊥FT and almost sl31it sequences in ⊥S, where addrS = Hom∧(f(F), T). Let A be an F-Gorenstein algebra, T a strong F-cotilting module and 0→A→B→C→0 and F-almost split sequence in ⊥FT.If the injective dimension of S as a Г-module is equal to d, then C≌(ΩCM^-dΩ^dDTrA^*)^*,where(-)^*=Hom(g,T).In addition, if the F-injective dimension of A is equal to d, then A≌ΩMF^-dDΩFop^-d TrC≌ΩCMF^-d ≌F^d DTrC. 相似文献
20.
The Besov spacesB
p
α,μ
(Γ) and Triebel-Lizorkin spacesF
p
α,μ
(Γ) with high order α∈R on a Lipschitz curve Γ are defined. when 1≤p≤∞, 1≤q≤∞. To compare to the classical case a difference
characterization of such spaces in the case |α|<1 is given also.
The author is supported in part by the Foundation of Zhongshan University Advanced Research Centre and NSF of China. 相似文献