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1.
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
2.
Jianwei Zhou 《Acta Mathematica Hungarica》2006,111(1-2):29-41
Summary We study minimal and totally geodesic submanifolds in Lie groups and related problems. We show that: (1) The imbedding of
the Grassmann manifold GF(n,N) in the Lie group GF(N) defined naturally makes GF(n,N) a totally geodesic submanifold; (2) The imbedding S7→SO(8) defined by octonians makes S7a totally geodesic submanifold inSO(8); (3) The natural inclusion of the Lie group GF(N) in the sphere ScN^2-1(√N) of gl(N,F)is minimal. Therefore the natural imbedding GF(N)<span style='font-size:10.0pt;font-family:"Lucida Sans Unicode"'>→gl(N,F)is formed by the eigenfunctions of the Laplacian on GF(N). 相似文献
3.
Lattice-universal Orlicz function spacesL
F
α,β[0, 1] with prefixed Boyd indices are constructed. Namely, given 0<α<β<∞ arbitrary there exists Orlicz function spacesL
F
α,β[0, 1] with indices α and β such that every Orlicz function spaceL
G
[0, 1] with indices between α and β is lattice-isomorphic to a sublattice ofL
F
α,β[0, 1]. The existence of classes of universal Orlicz spacesl
Fα,β(I) with uncountable symmetric basis and prefixed indices α and β is also proved in the uncountable discrete case.
Partially supported by BFM2001-1284. 相似文献
4.
We look at a special case of a familiar problem: Given a locally compact group G, a subgroup H and a complex representation π+ of G how does π+ decompose on restriction to H. Here G is GL+(2,F), where F is a nonarchimedian local field of characteristic not two, K a separable quadratic extension of F, GL+(2,F) the subgroup of index 2 in GL(2,F) consisting of those matrices whose determinant is in NK/F(K∗), π+ is an irreducible, admissible supercuspidal representation of GL+(2,F) and H=K∗ under an embedding of K∗ into GL(2,F). 相似文献
5.
The paper deals with the structure of intermediate subgroups of the general linear group GL(n, k) of degree n over a field k of odd characteristic that contain a nonsplit maximal torus related to a radical extension of degree n of the ground field k. The structure of ideal nets over a ring that determine the structure of intermediate subgroups containinga transvection
is given. Let K = k( n?{d} ) K = k\left( {\sqrt[n]{d}} \right) be a radical degree-n extension of a field k of odd characteristic, and let T =(d) be a nonsplit maximal torus, which is the image of the multiplicative group of the field K under the regular embedding in G =GL(n, k). In the paper, the structure of intermediate subgroups H, T ≤ H ≤ G, that contain a transvection is studied. The elements of the matrices in the torus T = T (d) generate a subring R(d) in the field k.Let R be an intermediate subring, R(d) ⊆ R ⊆ k, d ∈ R. Let σR denote the net in which the ideal dR stands on the principal diagonal and above it and all entries of which beneath the principal diagonal are equal to R. Let σR denote the net in which all positions on the principal diagonal and beneath it are occupied by R and all entries above the principal diagonal are equal to dR. Let E(σR) be the subgroup generated by all transvections from the net group G(σR). In the paper it is proved that the product TE(σR) is a group (and thus an intermediate subgroup). If the net σ associated with an intermediate subgroup H coincides with σR,then TE(σR) ≤ H ≤ N(σR),where N(σR) is the normalizer of the elementary net group E(σR) in G. For the normalizer N(σR),the formula N(σR)= TG(σR) holds. In particular, this result enables one to describe the maximal intermediate subgroups. Bibliography: 13 titles. 相似文献
6.
We call an element of a finite general linear group GL(d, q) fat if it leaves invariant and acts irreducibly on a subspace of dimension greater than d/2. Fatness of an element can be decided efficiently in practice by testing whether its characteristic polynomial has an irreducible
factor of degree greater than d/2. We show that for groups G with SL(d, q) ≤ G ≤ GL(d, q) most pairs of fat elements from G generate irreducible subgroups, namely we prove that the proportion of pairs of fat elements generating a reducible subgroup,
in the set of all pairs in G × G, is less than q
−d+1. We also prove that the conditional probability to obtain a pair (g
1, g
2) in G × G which generates a reducible subgroup, given that g
1, g
2 are fat elements, is less than 2q
−d+1. Further, we show that any reducible subgroup generated by a pair of fat elements acts irreducibly on a subspace of dimension
greater than d/2, and in the induced action the generating pair corresponds to a pair of fat elements. 相似文献
7.
Let F
p,t
(n) denote the number of the coefficients of (x
1+1x
2+...+x
t
)
j
, 0 ≤j≤n− 1, which are not divisible by the prime p. Define G
p,t
(n) = F
p,t
/n
θ and β(p,t) = lim infF
p,t
)(n)/n
θ, where θ = (log)/(log p). In this paper, we mainly prove that G
p,t
can be extended to a continuous function on ℝ+, and the function G
p,t
is nowhere monotonic. Both the set of differential points of the function G
p,t
and the set of non-differential points of the function G
p,t
are dense in ℝ+.
Received February 18, 2000, Accepted December 7, 2000 相似文献
8.
A three-valued function f: V → {−1, 0, 1} defined on the vertices of a graph G= (V, E) is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one.
That is, for every υ ∈ V, f(N(υ)) ⩾ 1, where N(υ) consists of every vertex adjacent to υ. The weight of an MTDF is f(V) = Σf(υ), over all vertices υ ∈ V. The minus total domination number of a graph G, denoted γ
t
−(G), equals the minimum weight of an MTDF of G. In this paper, we discuss some properties of minus total domination on a graph G and obtain a few lower bounds for γ
t
−(G). 相似文献
9.
Hamiltonism and Partially Square Graphs 总被引:10,自引:0,他引:10
Given a graph G, we define its partially square graph G
* as the graph obtained by adding edges uv whenever the vertices u and v have a common neighbor x satisfying the condition N
G[x]⊆N
G[u]∪N
G [v], where N
G[x]=N
G(x)∪{x}. In particular, this condition is satisfied if x does not center a claw (an induced K
1,3). Obviously G⊆G
*⊆G
2, where G
2 is the square of G. We prove that a k-connected graph (k≥2) G is hamiltonian if the independence number α(G
*) of G
* does not exceed k. If we replace G
* by G we get a well known result of Chvátal and Erdo?s. If G is claw-free and G
* is replaced by G
2 then we obtain a result of Ainouche, Broersma and Veldman. Relationships between connectivity of G and independence number of G
* for other hamiltonian properties are also given in this paper.
Received: June 17, 1996 Revised: October 30, 1998 相似文献
10.
Let F be a non-Archimedean locally compact field, and let p be its residual characteristic. Put G=GL
p
(F) and let G
′=D
×, where $D$ is a division algebra with centre F and of degree p
2 over F. The Jacquet–Langlands correspondence is a bijection between the discrete series of G and that of G
′. We describe this explicitly, in terms of Carayol's parametrization of these discrete series.
Received: 25 November 1999 相似文献
11.
Let G be a graph and W a subset of V(G). Let g,f:V(G)→Z be two integer-valued functions such that g(x)≤f(x) for all x∈V(G) and g(y)≡f(y) (mod 2) for all y∈W. Then a spanning subgraph F of G is called a partial parity (g,f)-factor with respect to W if g(x)≤deg
F
(x)≤f(x) for all x∈V(G) and deg
F
(y)≡f(y) (mod 2) for all y∈W. We obtain a criterion for a graph G to have a partial parity (g,f)-factor with respect to W. Furthermore, by making use of this criterion, we give some necessary and sufficient conditions for a graph G to have a subgraph which covers W and has a certain given property.
Received: June 14, 1999?Final version received: August 21, 2000 相似文献
12.
Yves Benoist 《Inventiones Mathematicae》2000,141(1):149-193
One studies the subgroups of GL(m,ℝ) which preserve a properly convex cone of ℝ
m
and whose action on ℝ
m
is irreducible. In particular, one describes the Zariski closure of these subgroups. As an application, one describes the
Zariski closure G of the subgroups of GL(m,ℝ) all of whose elements have nothing but positive eigenvalues. For instance, one can get the group G=GL(m,ℝ) if and only if m≠≡2 modulo4.
Oblatum 22-I-1999 & 10-XI-1999?Published online: 21 February 2000 相似文献
Automorphismes des c?nes convexes
Résumé. On étudie les sous-groupes de GL(m,ℝ) qui préservent un c?ne convexe saillant de ℝ m et dont l’action sur ℝ m est irréductible. En particulier, on décrit les adhérences de Zariski possibles pour ces sous-groupes. Comme application, on décrit les adhérences de Zariski G possibles pour les sous-groupes de GL(m,ℝ) dont tous les éléments ont toutes leurs valeurs propres positives. Par exemple, le groupe G=GL(m,ℝ) convient si et seulement si m≠≡2 modulo4.
Oblatum 22-I-1999 & 10-XI-1999?Published online: 21 February 2000 相似文献
13.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2009,7(2):176-185
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
相似文献
14.
David Helm 《Israel Journal of Mathematics》2012,187(1):37-80
Let G be a unitary group over ℚ, associated to a CM-field F with totally real part F
+, with signature (1, 1) at all the archimedean places of F
+. Under certain hypotheses on F
+, we show that Jacquet-Langlands correspondences between certain automorphic representations of G and representations of a group G′ isomorphic to G except at infinity can be realized in the cohomology of Shimura varieties attached to G and G′. 相似文献
15.
. In this work we consider finite undirected simple graphs. If G=(V,E) is a graph we denote by α(G) the stability number of G. For any vertex x let N[x] be the union of x and the neighborhood N(x). For each pair of vertices ab of G we associate the set J(a,b) as follows. J(a,b)={u∈N[a]∩N[b]∣N(u)⊆N[a]∪N[b]}. Given a graph G, its partially squareG
* is the graph obtained by adding an edge uv for each pair u,v of vertices of G at distance 2 whenever J(u,v) is not empty. In the case G is a claw-free graph, G
* is equal to G
2.
If G is k-connected, we cover the vertices of G by at most ⌈α(G
*)/k⌉ cycles, where α(G
*) is the stability number of the partially square graph of G. On the other hand we consider in G
* conditions on the sum of the degrees. Let G be any 2-connected graph and t be any integer (t≥2). If ∑
x
∈
S
deg
G
(x)≥|G|, for every t-stable set S⊆V(G) of G
* then the vertex set of G can be covered with t−1 cycles. Different corollaries on covering by paths are given.
Received: January 22, 1997 Final version received: February 15, 2000 相似文献
16.
Hervé Jacquet 《Israel Journal of Mathematics》1995,89(1-3):1-59
LetE/F be a quadratic extension of number fields,G the group GL(3,E) regarded as an algebraic group overF andU a quasi-split unitary group in three variables. Let alsoϑ be a generic character of a maximal unipotent subgroupN ofG. We derive an explicit expression for the integral
whereK
cont is the continuous part of the kernel attached to a smooth function of compact support onG(A). In particular, we prove that this expression is absolutely convergent. The result can be used to show that a cuspidal representation
ofG contains a vectorφ such thatεφ(u)du≠0 if and only if it is a base change from a representation of GL(3,F).
Partially supported by NSF Grant DMS-91-01637. 相似文献
17.
In the following,G denotes a finite group,r(G) the number of conjugacy classes ofG, β(G) the number of minimal normal subgroups ofG andα(G) the number of conjugate classes ofG not contained in the socleS(G). Let Φ
j
= {G|β(G) =r(G) −j}. In this paper, the family Φ11 is classified. In addition, from a simple inspection of the groups withr(G) =b conjugate classes that appear in ϒ
j
=1/11
Φ
j
, we obtain all finite groups satisfying one of the following conditions: (1)r(G) = 12; (2)r(G) = 13 andβ(G) > 1; …; (9)r(G) = 20 andβ(G) > 8; (10)r(G) =n andβ(G) =n −a with 1 ≦a ≦ 11, for each integern ≧ 21. Also, we obtain all finite groupsG with 13 ≦r(G) ≦ 20,β(G) ≦r(G) − 12, and satisfying one of the following conditions: (i) 0 ≦α(G) ≦ 4; (ii) 5 ≦α(G) ≦ 10 andS(G) solvable. 相似文献
18.
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
19.
F. Redig 《Bulletin of the Brazilian Mathematical Society》2002,33(3):427-446
We consider one-dimensional Gibbs measures on spin configurations σ ∈ {–1,+1}ℤ. For N ∈ ℕ let l
N
denote the length of the longest interval of consecutive spins of the same kind in the interval [0,N]. We show that the distribution of a suitable continuous modification l
c
(N) of l
N
converges to the Gumbel distribution, i.e., for some α, β ∈ (0, ∞) and γ ∈ ℝ,
lim
N
→∞ ℙ(l
c
(N) ≤ α log N + βx + γ) = e
–e
–x
.
Received: 2 September 2002 相似文献
20.
LetG be a unimodular Lie group, Γ a co-compact discrete subgroup ofG and ‘a’ a semisimple element ofG. LetT
a be the mapgΓ →ag Γ:G/Γ →G/Γ. The following statements are pairwise equivalent: (1) (T
a, G/Γ,θ) is weak-mixing. (2) (T
a, G/Γ) is topologically weak-mixing. (3) (G
u, G/Γ) is uniquely ergodic. (4) (G
u, G/Γ,θ) is ergodic. (5) (G
u, G/Γ) is point transitive. (6) (G
u, G/Γ) is minimal. If in additionG is semisimple with finite center and no compact factors, then the statement “(T
a, G/Γ,θ) is ergodic” may be added to the above list.
The authors were partially supported by NSF grant MCS 75-05250. 相似文献