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1.
Let G be a finite group and H a subgroup of G. We say that H is an ?-subgroup in G if NG(H) ∩ Hg ≤ H for all g ∈ G; H is called weakly ?-subgroup in G if G has a normal subgroup K such that G = HK and H ∩ K is an ?-subgroup in G. We say that H is weakly ? -embedded in G if G has a normal subgroup K such that HG = HK and H ∩ K is an ?-subgroup in G. In this paper, we investigate the structure of the finite group G under the assumption that some subgroups of prime power order are weakly ?-embedded in G. Our results improve and generalize several recent results in the literature. 相似文献
2.
Alessio Russo 《代数通讯》2013,41(10):3950-3954
A subgroup H of a group G is said to be weakly normal if H g = H whenever g is an element of G such that H g ≤ N G (H). There is a strictly relation between weak normality and groups in which normality is a transitive relation ( T-groups). In [Ballester-Bolinches, A., Esteban-Romero, R. (2003). On finite T-groups. J. Aust. Math. Soc. 75:181–191] it is proved that a finite group G is a soluble T-group if and only if every subgroup of G is weakly normal. In this article, we extend the above result to infinite groups having no infinite simple sections. Moreover, it will be shown that every locally graded non-periodic group, all of whose subgroups are weakly normal, is abelian. 相似文献
3.
Guizhen LIU 《Frontiers of Mathematics in China》2009,4(2):311-323
Let G be a digraph with vertex set V(G) and arc set E(G) and let g = (g
−, g
+) and ƒ = (ƒ
−, ƒ
+) be pairs of positive integer-valued functions defined on V(G) such that g
−(x) ⩽ ƒ
−(x) and g
+(x) ⩽ ƒ
+(x) for each x ∈ V(G). A (g, ƒ)-factor of G is a spanning subdigraph H of G such that g
−(x) ⩽ id
H
(x) ⩽ ƒ
−(x) and g
+(x) ⩽ od
H
(x) ⩽ ƒ
+(x) for each x ∈ V(H); a (g, ƒ)-factorization of G is a partition of E(G) into arc-disjoint (g, ƒ)-factors. Let
= {F
1, F
2,…, F
m} and H be a factorization and a subdigraph of G, respectively.
is called k-orthogonal to H if each F
i
, 1 ⩽ i ⩽ m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m−1,mƒ−m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k ⩽ min{g
−(x), g
+(x)} for any x ∈ V(G) and that every (mg, mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0 ⩽ g(x) ⩽ f(x) for any x ∈ V(G). The results in this paper are in some sense best possible.
相似文献
4.
Gordan Savin 《Israel Journal of Mathematics》1992,80(1-2):195-205
LetG andH ⊂G be two real semisimple groups defined overQ. Assume thatH is the group of points fixed by an involution ofG. Letπ ⊂L
2(H\G) be an irreducible representation ofG and letf επ be aK-finite function. Let Γ be an arithmetic subgroup ofG. The Poincaré seriesP
f(g)=ΣH∩ΓΓ
f(γ{}itg) is an automorphic form on Γ\G. We show thatP
f is cuspidal in some cases, whenH ∩Γ\H is compact.
Partially supported by NSF Grant # DMS 9103608. 相似文献
5.
Abhijit Pal 《Proceedings Mathematical Sciences》2010,120(1):57-68
Let 1 → (K, K
1) → (G, N
G
(K
1)) → (Q, Q
1) → 1 be a short exact sequence of pairs of finitely generated groups with K
1 a proper non-trivial subgroup of K and K strongly hyperbolic relative to K
1. Assuming that, for all g ∈ G, there exists k
g
∈ K such that gK
1
g
−1 = k
g
K
1
k
g−1, we will prove that there exists a quasi-isometric section s: Q → G. Further, we will prove that if G is strongly hyperbolic relative to the normalizer subgroup N
G
(K
1) and weakly hyperbolic relative to K
1, then there exists a Cannon-Thurston map for the inclusion i: Γ
K
→ Γ
G
. 相似文献
6.
XIAJIANGUO 《高校应用数学学报(英文版)》1998,13(1):109-116
Let E be a compact Lie group, G a closed subgroup of E, and H a closed normal sub-group of G. For principal fibre bundle (E,p, E,/G;G) tmd (E/H,p‘,E/G;G/H), the relation between auta(E) (resp. autce (E)) and autG/H(E/H) (resp. autGe/H(E/H)) is investigated by using bundle map theory and transformation group theory. It will enable us to compute the group JG(E) (resp. SG(E)) while the group J G/u(E/H) is known. 相似文献
7.
Suppose that H is a subgroup of a finite group G. H is called π-quasinormal in G if it permutes with every Sylow subgroup of G; H is called π-quasinormally embedded in G provided every Sylow subgroup of H is a Sylow subgroup of some π-quasinormal subgroup of G; H is called c-supplemented in G if there exists a subgroup N of G such that G = HN and H ∩ N ⩽ H
G
= Core
G
(H). In this paper, finite groups G satisfying the condition that some kinds of subgroups of G are either π-quasinormally embedded or c-supplemented in G, are investigated, and theorems which unify some recent results are given.
相似文献
8.
On Group Chromatic Number of Graphs 总被引:2,自引:0,他引:2
Let G be a graph and A an Abelian group. Denote by F(G, A) the set of all functions from E(G) to A. Denote by D an orientation of E(G). For f ∈ F(G,A), an (A,f)-coloring of G under the orientation D is a function c : V(G)↦A such that for every directed edge uv from u to v, c(u)−c(v) ≠ f(uv). G is A-colorable under the orientation D if for any function f ∈ F(G, A), G has an (A, f)-coloring. It is known that A-colorability is independent of the choice of the orientation. The group chromatic number of a graph G is defined to be the least positive integer m for which G is A-colorable for any Abelian group A of order ≥m, and is denoted by χg(G). In this note we will prove the following results. (1) Let H1 and H2 be two subgraphs of G such that V(H1)∩V(H2)=∅ and V(H1)∪V(H2)=V(G). Then χg(G)≤min{max{χg(H1), maxv∈V(H2)deg(v,G)+1},max{χg(H2), maxu∈V(H1) deg (u, G) + 1}}. We also show that this bound is best possible. (2) If G is a simple graph without a K3,3-minor, then χg(G)≤5. 相似文献
9.
Deguang Han 《Journal of Fourier Analysis and Applications》2009,15(2):201-217
Let
be a full rank time-frequency lattice in ℝ
d
×ℝ
d
. In this note we first prove that any dual Gabor frame pair for a Λ-shift invariant subspace M can be dilated to a dual Gabor frame pair for the whole space L
2(ℝ
d
) when the volume v(Λ) of the lattice Λ satisfies the condition v(Λ)≤1, and to a dual Gabor Riesz basis pair for a Λ-shift
invariant subspace containing M when v(Λ)>1. This generalizes the dilation result in Gabardo and Han (J. Fourier Anal. Appl. 7:419–433, [2001]) to both higher dimensions and dual subspace Gabor frame pairs. Secondly, for any fixed positive integer N, we investigate the problem whether any Bessel–Gabor family G(g,Λ) can be completed to a tight Gabor (multi-)frame G(g,Λ)∪(∪
j=1
N
G(g
j
,Λ)) for L
2(ℝ
d
). We show that this is true whenever v(Λ)≤N. In particular, when v(Λ)≤1, any Bessel–Gabor system is a subset of a tight Gabor frame G(g,Λ)∪G(h,Λ) for L
2(ℝ
d
). Related results for affine systems are also discussed.
Communicated by Chris Heil. 相似文献
10.
Yutaka Hiramine 《Designs, Codes and Cryptography》2009,50(3):285-290
Let D be an affine difference set of order n in an abelian group G relative to a subgroup N. Set = H \ {1, ω}, where H = G/N and . Using D we define a two-to-one map g from to N. The map g satisfies g(σ
m
) = g(σ)
m
and g(σ) = g(σ
−1) for any multiplier m of D and any element σ ∈ . As applications, we present some results which give a restriction on the possible order n and the group theoretic structure of G/N.
相似文献
11.
A finitely presented group G is hyperbolic iff H
(1)
1(G,ℝ)=0=(1)
2(G, ℝ), where H
(1)
* (resp. (1)
*) denotes the ℓ1-homology (resp. reduced ℓ1-homology). If Γ is a graph, then every ℓ1 1-cycle in Γ with real coefficients can be approximated by 1-cycles of compact support. A 1-relator group G is hyperbolic iff H
(1)
1(G,ℝ)=0.
Oblatum: 30-IV-1997 & 14-V-1998 / Published online: 14 January 1999 相似文献
12.
Gil Kaplan 《Israel Journal of Mathematics》1999,111(1):203-219
LetG be an arbitrary group with a subgroupA. The subdegrees of (A, G) are the indices [A:A ∪A
9] (wheregεG). Equivalent definitions of that concept are given in [IP] and [K]. IfA is not normal inG and all the subdegrees of (A, G) are finite, we attach to (A, G) the common divisor graph Γ: its vertices are the non-unit subdegrees of (A, G), and two different subdegrees are joined by an edge iff they arenot coprime. It is proved in [IP] that Γ has at most two connected components. Assume that Γ is disconnected. LetD denote the subdegree set of (A, G) and letD
1 be the set of all the subdegrees in the component of Γ containing min(D−{1}). We proved [K, Theorem A] that ifA is stable inG (a property which holds whenA or [G:A] is finite), then the setH={g ε G| [A:A ∪A
g
] εD
1 ∪ {1}} is a subgroup ofG. In this case we say thatA<H<G is a disconnected system (briefly: a system). In the current paper we deal with some fundamental types of systems. A systemA<H<G is irreducible if there does not exist 1<N△G such thatAN<H andAN/N<H/N<G/N is a system. Theorem A gives restrictions on the finite nilpotent normal subgroups ofG, whenG possesses an irreducible system. In particular, ifG is finite then Fit(G) is aq-group for a certain primeq. We deal also with general systems. Corollary (4.2) gives information about the structure of a finite groupG which possesses a system. Theorem B says that for any systemA<H<G,N
G
(N
G
(A))=N
G
(A). Theorem C and Corollary C’ generalize a result of Praeger [P, Theorem 2].
The content of this paper corresponds to a part of the author’s Ph.D. thesis carried out at Tel Aviv University under the
supervision of Prof. Marcel Herzog. 相似文献
13.
Harmonic maps with potential 总被引:8,自引:0,他引:8
Ali Fardoun Andrea Ratto 《Calculus of Variations and Partial Differential Equations》1997,5(2):183-197
Let (M,g) and (N,h) be two Riemannian manifolds, and G:N →ℝ a given function. If f:M → N is a smooth map, we set E
G
(f)=12 ∫M [∣df∣2− 2G(f)]dv
g. We establish some variational properties and some existence results for the functional E
G
(f): in particular, we analyse the case of maps into a sphere.
Received April 29, 1996 / Accepted May 28, 1996 相似文献
14.
Let G be a finite group. A subgroup H of G is called an ?-subgroup in G if N G (H) ∩ H x ≤ H for all x ∈ G. A subgroup H of G is called weakly ?-subgroup in G if there exists a normal subgroup K of G such that G = HK and H ∩ K is an ?-subgroup in G. In this article, we investigate the structure of the finite group G under the assumption that all maximal subgroups of every Sylow subgroup of some normal subgroup of G are weakly ?-subgroups in G. Some recent results are extended and generalized. 相似文献
15.
H. Karami S. M. Sheikholeslami Abdollah Khodkar Douglas B. West 《Graphs and Combinatorics》2012,28(1):123-131
A set S of vertices in a graph G is a connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by S is connected. The connected domination number
γ
c
(G) is the minimum size of such a set. Let d*(G)=min{d(G),d([`(G)])}{\delta^*(G)={\rm min}\{\delta(G),\delta({\overline{G}})\}} , where [`(G)]{{\overline{G}}} is the complement of G and δ(G) is the minimum vertex degree. We prove that when G and [`(G)]{{\overline{G}}} are both connected, gc(G)+gc([`(G)]) £ d*(G)+4-(gc(G)-3)(gc([`(G)])-3){{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \delta^*(G)+4-({\gamma_c}(G)-3)({\gamma_c}({\overline{G}})-3)} . As a corollary,
gc(G)+gc([`(G)]) £ \frac3n4{{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \frac{3n}{4}} when δ*(G) ≥ 3 and n ≥ 14, where G has n vertices. We also prove that gc(G)+gc([`(G)]) £ d*(G)+2{{\gamma_c}(G)+{\gamma_c}({\overline{G}})\le \delta^*(G)+2} when gc(G),gc([`(G)]) 3 4{{\gamma_c}(G),{\gamma_c}({\overline{G}})\ge 4} . This bound is sharp when δ*(G) = 6, and equality can only hold when δ*(G) = 6. Finally, we prove that gc(G)gc([`(G)]) £ 2n-4{{\gamma_c}(G){\gamma_c}({\overline{G}})\le 2n-4} when n ≥ 7, with equality only for paths and cycles. 相似文献
16.
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ⩽ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S
4-free and every minimal subgroup of P ∩ G
N
is c-supplemented in N
G
(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized. 相似文献
17.
Let G = GL
N
or SL
N
as reductive linear algebraic group over a field k of characteristic p > 0. We prove several results that were previously established only when N ⩽ 5 or p > 2
N
: Let G act rationally on a finitely generated commutative k-algebra A and let grA be the Grosshans graded ring. We show that the cohomology algebra H
*(G, grA) is finitely generated over k. If moreover A has a good filtration and M is a Noetherian A-module with compatible G action, then M has finite good filtration dimension and the H
i
(G, M) are Noetherian A
G
-modules. To obtain results in this generality, we employ functorial resolution of the ideal of the diagonal in a product
of Grassmannians. 相似文献
18.
Simple graphs are considered. Let G be a graph andg(x) andf(x) integer-valued functions defined on V(G) withg(x)⩽f(x) for everyxɛV(G). For a subgraphH ofG and a factorizationF=|F
1,F
2,⃛,F
1| ofG, if |E(H)∩E(F
1)|=1,1⩽i⩽j, then we say thatF orthogonal toH. It is proved that for an (mg(x)+k,mf(x) -k)-graphG, there exists a subgraphR ofG such that for any subgraphH ofG with |E(H)|=k,R has a (g,f)-factorization orthogonal toH, where 1⩽k<m andg(x)⩾1 orf(x)⩾5 for everyxɛV(G).
Project supported by the Chitia Postdoctoral Science Foundation and Chuang Xin Foundation of the Chinese Academy of Sciences. 相似文献
19.
Noga Alon 《Israel Journal of Mathematics》1986,53(1):97-120
All graphs considered are finite, undirected, with no loops, no multiple edges and no isolated vertices. For two graphsG, H, letN(G, H) denote the number of subgraphs ofG isomorphic toH. Define also, forl≧0,N(l, H)=maxN(G, H), where the maximum is taken over all graphsG withl edges. We determineN(l, H) precisely for alll≧0 whenH is a disjoint union of two stars, and also whenH is a disjoint union ofr≧3 stars, each of sizes ors+1, wheres≧r. We also determineN(l, H) for sufficiently largel whenH is a disjoint union ofr stars, of sizess
1≧s
2≧…≧s
r>r, provided (s
1−s
r)2<s
1+s
r−2r. We further show that ifH is a graph withk edges, then the ratioN(l, H)/l
k tends to a finite limit asl→∞. This limit is non-zero iffH is a disjoint union of stars. 相似文献
20.
Let H\G be a causal symmetric space sitting inside its complexification H
ℂ\G
ℂ. Then there exist certain G-invariant Stein subdomains Ξ of H
ℂ\G
ℂ. The Haar measure on H
ℂ\G
ℂ gives rise to a G-invariant measure on Ξ. With respect to this measure one can define the Bergman space B
2(Ξ) of square integrable holomorphic functions on Ξ. The group G acts unitarily on the Hilbert space B
2(Ξ) by left translations in the arguments. The main result of this paper is the Plancherel Theorem for B
2(Ξ), i.e., the disintegration formula for the left regular representation into irreducibles.
Received: Received: 23 November 1998 相似文献