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1.
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.
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.
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   

5.
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   

6.
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≤iDi. 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   

7.
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   

8.
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 XG 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   

9.
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≤ rank G.  相似文献   

10.
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