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1.
It is proved that, if G is a finite group that has the same set of element orders as the simple group C p (2) for prime p > 3, then G/O 2(G) is isomorphic to C p (2).  相似文献   

2.
In this paper we consider n-poised planar node sets, as well as more special ones, called G C n sets. For the latter sets each n-fundamental polynomial is a product of n linear factors as it always holds in the univariate case. A line ? is called k-node line for a node set \(\mathcal X\) if it passes through exactly k nodes. An (n + 1)-node line is called maximal line. In 1982 M. Gasca and J. I. Maeztu conjectured that every G C n set possesses necessarily a maximal line. Till now the conjecture is confirmed to be true for n ≤ 5. It is well-known that any maximal line M of \(\mathcal X\) is used by each node in \(\mathcal X\setminus M, \)meaning that it is a factor of the fundamental polynomial. In this paper we prove, in particular, that if the Gasca-Maeztu conjecture is true then any n-node line of G C n set \(\mathcal {X}\) is used either by exactly \(\binom {n}{2}\) nodes or by exactly \(\binom {n-1}{2}\) nodes. We prove also similar statements concerning n-node or (n ? 1)-node lines in more general n-poised sets. This is a new phenomenon in n-poised and G C n sets. At the end we present a conjecture concerning any k-node line.  相似文献   

3.
The following results are obtained: (1) a criterion for the separability of the space of continuous functions C(X) with the set-open topology; (2) a criterion for the sequential separability of the space Cp(A|X), where A ? X; (3) an answer to Velichko’s question of whether a set-theoretic condition on a metric space X in a criterion for the sequential separability of Cp(X) is necessary.  相似文献   

4.
Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p and p′ are joined by an edge if there is an element in G of order pp′. We denote by k(Γ(G)) the number of isomorphism classes of finite groups H satisfying Γ(G) = Γ(H). Given a natural number r, a finite group G is called r-recognizable by prime graph if k(Γ(G)) =  r. In Shen et al. (Sib. Math. J. 51(2):244–254, 2010), it is proved that if p is an odd prime, then B p (3) is recognizable by element orders. In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(B p (3)), where p > 3 is an odd prime, then \({G\cong B_p(3)}\) or C p (3). Also if Γ(G) = Γ(B 3(3)), then \({G\cong B_3(3), C_3(3), D_4(3)}\), or \({G/O_2(G)\cong {\rm Aut}(^2B_2(8))}\). As a corollary, the main result of the above paper is obtained.  相似文献   

5.
If T is a multiplicity-free contraction of class C 0 with minimal function m T , then it is quasisimilar to the Jordan block S(m T ). In case m T is a Blaschke product with simple roots forming a Carleson sequence, we show that the relation between T and S(m T ) can be strengthened to similarity. Under the additional assumption that u(T) has closed range for every inner divisor \({u\in H^\infty}\) of m T , the result also holds in the more general setting where the roots have bounded multiplicities.  相似文献   

6.
We show that if K is a compact metric space then C(K) is a 2-absolute Lipschitz retract. We then study the best Lipschitz extension constants for maps into C(K) from a given metric space M, extending recent results of Lancien and Randrianantoanina. They showed that a finite-dimensional normed space which is polyhedral has the isometric extension property for C(K)-spaces; here we show that the same result holds for spaces with Gateaux smooth norm or of dimension two; a three-dimensional counterexample is also given. We also show that X is polyhedral if and only if every subset E of X has the universal isometric extension property for C(K)-spaces. We also answer a question of Naor on the extension of Hölder continuous maps.  相似文献   

7.
Let T t : XX be a C 0-semigroup with generator A. We prove that if the abscissa of uniform boundedness of the resolvent s 0(A) is greater than zero then for each nondecreasing function h(s): ?+R + there are x′X′ and xX satisfying ∫ 0 h(|〈x′, T x x〉|)dt = ∞. If i? ∩ Sp(A) ≠ Ø then such x may be taken in D(A ).  相似文献   

8.
In this paper we show that if \({S\in L(X,Y)}\) and \({R\in L(Y,X),}\) X and Y complex Banach spaces, then the products RS and SR share the Dunford property (C). We also study property (C) for R, S, RS and \({SR \in L(X)}\) in the case that R and S satisfies the operator equations RSR = R 2 and SRS = S 2.  相似文献   

9.
Let C(M) be the space of all continuous functions on M? ?. We consider the multiplication operator T: C(M) → C(M) defined by Tf(z) = zf(z) and the torus
$$O(M) = \left\{ {f:M \to \mathbb{C} \ntrianglelefteq \left\| f \right\| = \left\| {\frac{1}{f}} \right\| = 1} \right\}$$
. If M is a Kronecker set, then the T-orbits of the points of the torus ½O(M) are dense in ½O(M) and are ½-dense in the unit ball of C(M).
  相似文献   

10.
A subgroup K of G is Mp-supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = pα. In this paper we prove the following: Let p be a prime divisor of |G| and let H be ap-nilpotent subgroup having a Sylow p-subgroup of G. Suppose that H has a subgroup D with Dp ≠ 1 and |H: D| = pα. Then G is p-nilpotent if and only if every subgroup T of H with |T| = |D| is Mp-supplemented in G and NG(Tp)/CG(Tp) is a p-group.  相似文献   

11.
We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.  相似文献   

12.
Let G be a simple graph, let d(v) denote the degree of a vertex v and let g be a nonnegative integer function on V (G) with 0 ≤ g(v) ≤ d(v) for each vertex vV (G). A g c -coloring of G is an edge coloring such that for each vertex vV (G) and each color c, there are at least g(v) edges colored c incident with v. The g c -chromatic index of G, denoted by χ′g c (G), is the maximum number of colors such that a gc-coloring of G exists. Any simple graph G has the g c -chromatic index equal to δ g (G) or δ g (G) ? 1, where \({\delta _g}\left( G \right) = \mathop {\min }\limits_{v \in V\left( G \right)} \left\lfloor {d\left( v \right)/g\left( v \right)} \right\rfloor \). A graph G is nearly bipartite, if G is not bipartite, but there is a vertex uV (G) such that G ? u is a bipartite graph. We give some new sufficient conditions for a nearly bipartite graph G to have χ′g c (G) = δ g (G). Our results generalize some previous results due to Wang et al. in 2006 and Li and Liu in 2011.  相似文献   

13.
We introduce the notion of property (RD) for a locally compact, Hausdorff and r-discrete groupoid G, and show that the set S 2 l (G) of rapidly decreasing functions on G with respect to a continuous length function l is a dense spectral invariant and Fréchet *-subalgebra of the reduced groupoid C*-algebra C r * (G) of G when G has property (RD) with respect to l, so the K-theories of both algebras are isomorphic under inclusion. Each normalized cocycle c on G, together with an invariant probability measure on the unit space G 0 of G, gives rise to a canonical map τ c on the algebra C c (G) of complex continuous functions with compact support on G. We show that the map τ c can be extended continuously to S 2 l (G) and plays the same role as an n-trace on C r * (G) when G has property (RD) and c is of polynomial growth with respect to l, so the Connes’ fundament paring between the K-theory and the cyclic cohomology gives us the K-theory invariants on C r * (G).  相似文献   

14.
An edge-coloring of a graph G is an assignment of colors to all the edges of G. A g c -coloring of a graph G is an edge-coloring of G such that each color appears at each vertex at least g(v) times. The maximum integer k such that G has a g c -coloring with k colors is called the g c -chromatic index of G and denoted by \(\chi\prime_{g_{c}}\)(G). In this paper, we extend a result on edge-covering coloring of Zhang and Liu in 2011, and give a new sufficient condition for a simple graph G to satisfy \(\chi\prime_{g_{c}}\)(G) = δ g (G), where \(\delta_{g}\left(G\right) = min_{v\epsilon V (G)}\left\{\lfloor\frac{d\left(v\right)}{g\left(v\right)}\rfloor\right\}\).  相似文献   

15.
A Coxeter system (W, S) is said to be of type K n if the associated Coxeter graph ΓS is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by ΓS. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type K n then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W).  相似文献   

16.
Given an indexing set I and a finite field Kα for each α ∈ I, let ? = {L2(Kα) | α ∈ I} and \(\mathfrak{N} = \{ SL_2 (K_\alpha )|\alpha \in I\}\). We prove that each periodic group G saturated with groups in \(\Re (\mathfrak{N})\) is isomorphic to L2(P) (respectively SL2(P)) for a suitable locally finite field P.  相似文献   

17.
Let (F k,n ) n and (L k,n )n be the k-Fibonacci and k-Lucas sequence, respectively, which satisfies the same recursive relation a n+1 = ka n + a n?1 with initial values F k,0 = 0, F k,1 = 1, L k,0 = 2 and L k,1 = k. In this paper, we characterize the p-adic orders ν p (F k,n ) and ν p (L k,n ) for all primes p and all positive integers k.  相似文献   

18.
The C*-simplicity of n-periodic products is proved for a large class of groups. In particular, the n-periodic products of any finite or cyclic groups (including the free Burnside groups) are C*-simple. Continuum-many nonisomorphic 3-generated nonsimple C*-simple groups are constructed in each of which the identity xn = 1 holds, where n ≥ 1003 is any odd number. The problem of the existence of C*-simple groups without free subgroups of rank 2 was posed by de la Harpe in 2007.  相似文献   

19.
Let G be a nonabelian group, and associate the noncommuting graph ?(G) with G as follows: the vertex set of ?(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. Let S 4(q) be the projective symplectic simple group, where q is a prime power. We prove that if G is a group with ?(G) ? ?(S 4(q)) then G ? S 4(q).  相似文献   

20.
Let λK m,n be a complete bipartite multigraph with two partite sets having m and n vertices, respectively. A K p,q -factorization of λK m,n is a set of edge-disjoint K p,q -factors of λK m,n which partition the set of edges of λK m,n . When p = 1 and q is a prime number, Wang, in his paper [On K 1,q -factorization of complete bipartite graph, Discrete Math., 126: (1994), 359-364], investigated the K 1,q -factorization of K m,n and gave a sufficient condition for such a factorization to exist. In papers [K 1,k -factorization of complete bipartite graphs, Discrete Math., 259: 301-306 (2002),; K p,q -factorization of complete bipartite graphs, Sci. China Ser. A-Math., 47: (2004), 473-479], Du and Wang extended Wang’s result to the case that p and q are any positive integers. In this paper, we give a sufficient condition for λK m,n to have a K p,q -factorization. As a special case, it is shown that the necessary condition for the K p,q -factorization of λK m,n is always sufficient when p : q = k : (k + 1) for any positive integer k.  相似文献   

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