共查询到20条相似文献,搜索用时 15 毫秒
1.
Edith Adan-Bante 《Archiv der Mathematik》2005,85(4):297-303
Let G be a finite p-group, where p is a prime number, and a ∈ G. Denote by Cl(a) = {gag−1| g ∈ G} the conjugacy class of a in G. Assume that |Cl(a)| = pn. Then Cl(a) Cl(a−1) = {xy | x ∈ Cl(a), y ∈ Cl(a−1)} is the union of at least n(p − 1) + 1 distinct conjugacy classes of G.
Received: 16 December 2004 相似文献
2.
A. Ballester-Bolinches John Cossey R. Esteban-Romero 《Annali di Matematica Pura ed Applicata》2010,189(4):567-570
For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes ${\mathcal {A}, \mathcal {B}}For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B{\mathcal {A}, \mathcal {B}} are joined by an edge if for some A ? A, B ? B A{A \in \mathcal {A},\, B \in \mathcal {B}\, A} and B permute. We characterise those groups G for which Γ(G) is complete. 相似文献
3.
We show that a finite generalized polygon Γ is Moufang with respect to a groupG if and only if for every flag {x, y} of Γ, the subgroupG
1(x, y) ofG fixing every element incident with one ofx, y acts transitively on the set of apartments containing the elementsu, x, y, w, whereu≠y (resp.w≠x) is an arbitrary element incident withx (resp.y).
Research Associate at the National Fund of Scientific Research of Belgium.
Research partially supported by NSF Grant DMS-8901904. 相似文献
4.
For a finite group G and a non-linear irreducible complex character χ of G write υ(χ) = {g ∈ G | χ(g) = 0}. In this paper, we study the finite non-solvable groups G such that υ(χ) consists of at most two conjugacy classes for all but one of the non-linear irreducible characters χ of G. In particular, we characterize a class of finite solvable groups which are closely related to the above-mentioned question
and are called solvable φ-groups. As a corollary, we answer Research Problem 2 in [Y.Berkovich and L.Kazarin: Finite groups in which the zeros of every
non-linear irreducible character are conjugate modulo its kernel. Houston J. Math. 24 (1998), 619–630.] posed by Y.Berkovich
and L.Kazarin. 相似文献
5.
Kazuhide Hirohata 《Graphs and Combinatorics》2000,16(3):269-273
Let G be a 2-connected graph with maximum degree Δ (G)≥d, and let x and y be distinct vertices of G. Let W be a subset of V(G)−{x, y} with cardinality at most d−1. Suppose that max{d
G(u), d
G(v)}≥d for every pair of vertices u and v in V(G)−({x, y}∪W) with d
G(u,v)=2. Then x and y are connected by a path of length at least d−|W|.
Received: February 5, 1998 Revised: April 13, 1998 相似文献
6.
O. A. Alekseeva A. S. Kondrat’ev 《Proceedings of the Steklov Institute of Mathematics》2009,266(Z1):10-23
It is proved that, if G is a finite group that has the same set of element orders as the simple group D
p
(q), where p is prime, p ≥ 5 and q ∈ {2, 3, 5}, then the commutator group of G/F(G) is isomorphic to D
p
(q), the subgroup F(G) is equal to 1 for q = 5 and to O
q
(G) for q ∈ {2, 3}, F(G) ≤ G′, and |G/G′| ≤ 2. 相似文献
7.
Let p(G) and c(G) denote the number of vertices in a longest path and a longest cycle, respectively, of a finite, simple graph G. Define σ4(G)=min{d(x
1)+d(x
2)+ d(x
3)+d(x
4) | {x
1,…,x
4} is independent in G}. In this paper, the difference p(G)−c(G) is considered for 2-connected graphs G with σ4(G)≥|V(G)|+3. Among others, we show that p(G)−c(G)≤2 or every longest path in G is a dominating path.
Received: August 28, 2000 Final version received: May 23, 2002 相似文献
8.
Let G be a graph and S ⊂ V(G). We denote by α(S) the maximum number of pairwise nonadjacent vertices in S. For x, y ∈ V(G), the local connectivity κ(x, y) is defined to be the maximum number of internally-disjoint paths connecting x and y in G. We define . In this paper, we show that if κ(S) ≥ 3 and for every independent set {x
1, x
2, x
3, x
4} ⊂ S, then G contains a cycle passing through S. This degree condition is sharp and this gives a new degree sum condition for a 3-connected graph to be hamiltonian. 相似文献
9.
For any vertex u∈V(G), let T_N(U)={u}∪{uv|uv∈E(G), v∈v(G)}∪{v∈v(G)|uv∈E(G)}and let f be a total k-coloring of G. The total-color neighbor of a vertex u of G is the color set C_f(u)={f(x)|x∈TN(U)}. For any two adjacent vertices x and y of V(G)such that C_f(x)≠C_f(y), we refer to f as a k-avsdt-coloring of G("avsdt"is the abbreviation of"adjacent-vertex-strongly- distinguishing total"). The avsdt-coloring number of G, denoted by X_(ast)(G), is the minimal number of colors required for a avsdt-coloring of G. In this paper, the avsdt-coloring numbers on some familiar graphs are studied, such as paths, cycles, complete graphs, complete bipartite graphs and so on. We proveΔ(G) 1≤X_(ast)(G)≤Δ(G) 2 for any tree or unique cycle graph G. 相似文献
10.
Let G be a nonabelian group. We define the noncommuting graph ∇(G) of G as follows: its vertex set is G\Z(G), the set of non-central elements of G, and two different vertices x and y are joined by an edge if and only if x and y do not commute as elements of G, i.e., [x, y] ≠ 1. We prove that if L ∈ {L
4(7), L
4(11), L
4(13), L
4(16), L
4(17)} and G is a finite group such that ∇(G) ≅ ∇(L), then G ≅ L. 相似文献
11.
For a finite group G, let v(G) denote the number of conjugacy classes of non-normal subgroups of G and vc(G) denote the number of conjugacy classes of non-normal noncyclic subgroups of G. In this paper, we show that every finite group G satisfying v(G) ≤2|π(G)| or vc(G) ≤ |π(G)| is solvable, and for a finite nonsolvable group G, v(G) = 2|π(G)| +1 if and only if G ? A 5. 相似文献
12.
In 1990 G. T. Chen proved that if G is a 2-connected graph of order n and 2|N(x) ∪ N(y)| + d(x) + d(y) ≥ 2n − 1 for each pair of nonadjacent vertices x, y ∈ V (G), then G is Hamiltonian. In this paper we prove that if G is a 2-connected graph of order n and 2|N(x) ∪ N(y)| + d(x)+d(y) ≥ 2n−1 for each pair of nonadjacent vertices x, y ∈ V (G) such that d(x, y) = 2, then G is Hamiltonian. 相似文献
13.
Summary LetX be the observed vector of thep-variate (p≧3) normal distribution with mean θ and covariance matrix equal to the identity matrix. Denotey
+=max{0,y} for any real numbery. We consider the confidence set estimator of θ of the formC
δa,φ={θ:|θ−δa,φ(X)}≦c}, whereδ
a,φ=[1−aφ({X})/{X}2]+X is the positive part of the Baranchik (1970,Ann. Math. Statist.,41, 642–645) estimator. We provide conditions on ϕ(•) anda which guarantee thatC
δa.φ has higher coverage probability than the usual one, {θ:|θ−X|≦c}. This dominance result will be shown to hold for spherically symmetric distributions, which include the normal distribution,t-distribution and double exponential distribution. The latter result generalizes that of Hwang and Chen (1983,Technical Report, Dept. of Math., Cornell University). 相似文献
14.
Let G be an infinite graph embedded in a closed 2-manifold, such that each open face of the embedding is homeomorphic to an open
disk and is bounded by finite number of edges. For each vertex x of G, define the combinatorial curvature
as that of [8], where d(x) is the degree of x, F(x) is the multiset of all open faces σ in the embedding such that the closure contains x (the multiplicity of σ is the number of times that x is visited along ∂σ), and |σ| is the number of sides of edges bounding the face σ. In this paper, we first show that if the
absolute total curvature ∑
x∈V(G) |Φ
G
(x)| is finite, then G has only finite number of vertices of non-vanishing curvature. Next we present a Gauss-Bonnet formula for embedded infinite
graphs with finite number of accumulation points. At last, for a finite simple graph G with 3 ≤ d
G
(x) < ∞ and Φ
G
(x) > 0 for every x ∈ V(G), we have (i) if G is embedded in a projective plane and #(V(G)) = n ≥ 1722, then G is isomorphic to the projective wheel P
n
; (ii) if G is embedded in a sphere and #(V(G)) = n ≥ 3444, then G is isomorphic to the sphere annulus either A
n
or B
n
; and (iii) if d
G
(x) = 5 for all x ∈ V(G), then there are only 49 possible embedded plane graphs and 16 possible embedded projective plane graphs.
Guantao Chen: The second author was partially supported by NSF DMS-0070514 and NSA-H98230-04-1-0300. 相似文献
15.
Chmielinski has proved in the paper [4] the superstability of the generalized orthogonality equation |〈f(x), f(y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmielinski by proving a theorem: LetD
n be a suitable subset of ℝn. If a function f:D
n → ℝn satisfies the inequality ∥〈f(x), f(y)〉| |〈x,y〉∥ ≤ φ(x,y) for an appropriate control function φ(x, y) and for allx, y ∈ D
n, thenf satisfies the generalized orthogonality equation for anyx, y ∈ D
n. 相似文献
16.
For a finite poset P = (V, ≤ ), let _s(P){\cal B}_s(P) consist of all triples (x,y,z) ∈ V
3 such that either x < y < z or z < y < x. Similarly, for every finite, simple, and undirected graph G = (V,E), let Bs(G){\cal B}_s(G) consist of all triples (x,y,z) ∈ V
3 such that y is an internal vertex on an induced path in G between x and z. The ternary relations Bs(P){\cal B}_s(P) and Bs(G){\cal B}_s(G) are well-known examples of so-called strict betweennesses. We characterize the pairs (P,G) of posets P and graphs G on the same ground set V which induce the same strict betweenness relation Bs(P)=Bs(G){\cal B}_s(P)={\cal B}_s(G). 相似文献
17.
Akira Saito 《Combinatorica》1996,16(3):433-437
A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg
G
x
, deg
G
y
}k for every pair of verticesx,y withd
G
(x,y)=2 in a 2-connected graphG, whered
G
(x,y) is the distance betweenx andy inG, thenG isk-path-connected. 相似文献
18.
In this paper we deal with ordinary differential equations of the form dy/dx = P(x, y) where P(x, y) is a real polynomial in the variables x and y, of degree n in the variable y. If y = φ(x) is a solution of this equation defined for x ∈ [0, 1] and which satisfies φ(0) = φ(1), we say that it is a periodic orbit. A limit cycle is an isolated periodic orbit in the set of all periodic orbits. If
φ(x) is a polynomial, then φ(x) is called a polynomial solution. 相似文献
19.
Rossitza I. Semerdjieva 《Mathematische Nachrichten》2002,237(1):89-104
Let k(y) > 0, 𝓁(y) > 0 for y > 0, k(0) = 𝓁(0) = 0 and limy → 0k(y)/𝓁(y) exists; then the equation L(u) ≔ k(y)uxx – ∂y(𝓁(y)uy) + a(x, y)ux = f(x, y, u) is strictly hyperbolic for y > 0 and its order degenerates on the line y = 0. Consider the boundary value problem Lu = f(x, y, u) in G, u|AC = 0, where G is a simply connected domain in ℝ2 with piecewise smooth boundary ∂G = AB∪AC∪BC; AB = {(x, 0) : 0 ≤ x ≤ 1}, AC : x = F(y) = ∫y0(k(t)/𝓁(t))1/2dt and BC : x = 1 – F(y) are characteristic curves. Existence of generalized solution is obtained by a finite element method, provided f(x, y, u) satisfies Carathéodory condition and |f(x, y, u)| ≤ Q(x, y) + b|u| with Q ∈ L2(G), b = const > 0. It is shown also that each generalized solution is a strong solution, and that fact is used to prove uniqueness under the additional assumption |f(x, y, u1) – f(x, y, u2| ≤ C|u1 – u2|, where C = const > 0. 相似文献
20.
We prove a “unique crossed product decomposition” result for group measure space II1 factors L ∞(X)⋊Γ arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups Γ in a fairly large family
G\mathcal{G}, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products
over an amenable subgroup. We deduce that if T
n
denotes the group of upper triangular matrices in PSL (n,ℤ), then any free, mixing p.m.p. action of
G = \operatornamePSL(n,\mathbbZ)*Tn\operatornamePSL(n,\mathbbZ)\Gamma=\operatorname{PSL}(n,\mathbb{Z})*_{T_{n}}\operatorname{PSL}(n,\mathbb{Z}) is W∗-superrigid, i.e. any isomorphism between L ∞(X)⋊Γ and an arbitrary group measure space factor L ∞(Y)⋊Λ, comes from a conjugacy of the actions. We also prove that for many groups Γ in the family G\mathcal{G}, the Bernoulli actions of Γ are W∗-superrigid. 相似文献