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1.
A bijective mapping
defined on a finite group G is complete if the mapping defined by
,
, is bijective. In 1955 M. Hall and L. J. Paige conjectured that a finite group G has a complete mapping if and only if a Sylow 2-subgroup of G is non-cyclic or trivial. This conjecture is still open. In this paper we construct a complete mapping for the projective groups PSL
and PGL(2,q),q odd. As a consequence, we prove that in odd characteristic the projective groups PGL(n,q GL
, admit a complete mapping. 相似文献
2.
TATSUYA MARUTA 《Geometriae Dedicata》1997,65(3):299-304
Let
be the smallest integer n for which there exists a linear code of length n, dimension k and minimum Hamming distance d over the Galois field GF(q). In this paper we determine
for
for all q, using a geometric method. 相似文献
3.
Yutaka Hiramine 《Geometriae Dedicata》1993,48(2):139-189
In this paper we consider finite nets of orderq
2 and degreeq + 1 which admit GL(2,q). Our main result says that if a net
of orderq
2 and degreeq + 1 admits a collineation group with a point-regular normal subgroupT such that /T GL(2,q), then
is isomorphic to a regulus net, a twisted regulus net, a Hering net, or
. Except in the last one, each of them corresponds to a surface in PG(3,q) obtained from a homogeneous polynomial in two variables. 相似文献
4.
Albrecht Beutelspacher 《Geometriae Dedicata》1980,9(4):425-449
A t-blocking set in the finite projective space PG(d, q) with dt+1 is a set
of points such that any (d–t)-dimensional subspace is incident with a point of
and no t-dimensional subspace is contained in
. It is shown that |
|q
t
+...+1+q
t–1q and the examples of minimal cardinality are characterized. Using this result it is possible to prove upper and lower bounds for the cardinality of partial t-spreads in PG(d, q). Finally, examples of blocking sets and maximal partial spreads are given. 相似文献
5.
Marilyn Breen 《Geometriae Dedicata》1996,60(3):283-288
Let
be a family of simple polygons in the plane. If every three (not necessarily distinct) members of
have a simply connected union and every two members of
have a nonempty intersection, then {P:P in
}
. Applying the result to a finite family
of orthogonally convex polygons, the set {C:C in
} will be another orthogonally convex polygon, and, in certain circumstances, the dimension of this intersection can be determined.Supported in part by NSF grant DMS-9207019. 相似文献
6.
A submanifold M
n
r
of Minkowski space
is said to be of restricted type if its shape operator with respect to the mean curvature vector is the restriction of a fixed linear transformation of
to the tangent space of M
n
r
at every point of M
n
r
. In this paper we completely classify hypersurfaces of restricted type in
. More precisely, we prove that a hypersurface of
is of restricted type if and only if it is either a minimal hypersurface, or an open part of one of the following hypersurfaces: S
k
×
, S
k
1
×
, H
k
×
, S
n
1
, H
n
, with 1kn–1, or an open part of a cylinder on a plane curve of restricted type.This work was done when the first and fourth authors were visiting Michigan State University.Aangesteld Navorser N.F.W.O., Belgium. 相似文献
7.
Chihiro Suetake 《Geometriae Dedicata》1994,51(2):123-131
Let be a translation plane of orderq
3,q an odd prime power, whose kern GF(q). Letl
be the line at infinity of . LetG be a solvable collineation group of in the linear translation complement, which acts transitively onl
, and letH be a maximal normal cyclic subgroup ofG. Then the restriction
ofH onl
acts semiregularly onl
and
{1, 2, 3, 6}, where
is the restriction ofG onl
(ifq –1(mod 3), then
{1, 2}). Ifq {3, 5} and
{1, 2}, then is determined completely, using a computer. 相似文献
8.
Rudolf Scharlau 《Geometriae Dedicata》1987,24(1):77-84
Following earlier work of Tits [8], this paper deals with the structure of buildings which are not necessarily thick; that is, possessing panels (faces of codimension 1) which are contained in two chambers, only. To every building , there is canonically associated a thick building
whose Weyl group W(
) can be considered as a reflection subgroup of the Weyl group W() of . One can reconstruct from
together with the embedding W(
) W(). Conversely, if
is any thick building and W any reflection group containing W(
) as a reflection subgroup, there exists a weak building with Weyl group W and associated thick building
. 相似文献
9.
J. M. Wills 《Geometriae Dedicata》1991,40(2):237-244
For the lattice point enumerator of a lattice
and a convex body K we give bounds in terms of the intrinsic volumes of K and of minimal determinants of
. The intrinsic volumes are the normalized Minkowski quermassintegrals and the minimal determinants are analogous functionals of
. 相似文献
10.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
11.
We study level surfaces of non-degenerate functions inR
n+1. Such level surfaces are non-degenerate in the sense of affine differential geometry. In affine differential geometry, the affine normal plays an important role for the study of a non-degenerate hypersurface. In this note, being motivated by Koszul's work we take a canonical vector field
for level surfaces of a non-degenerate function and give certain characterizations of when
is transversal, by the shape operatorS, the transversal connection , and consider the difference between
and the affine normal. 相似文献
12.
Giuseppe Zampieri 《Compositio Mathematica》2000,121(2):155-161
For a domain of
we introduce a fairly general and intrinsic condition of weak q-pseudoconvexity, and prove, in Theorem 4, solvability of the
-complex for forms with
-coefficients in degree
. All domains whose boundary have a constant number of negative Levi eigenvalues are easily recognized to fulfill our condition of q-pseudoconvexity; thus we regain the result of Michel (with a simplified proof). Our method deeply relies on the L
2-estimates by Hörmander (with some variants). The main point of our proof is that our estimates (both in weightened-L
2 and in Sobolev norms) are sufficiently accurate to permit us to exploit the technique by Dufresnoy for regularity up to the boundary. 相似文献
13.
Alessandra Celletti Piero Negrini 《NoDEA : Nonlinear Differential Equations and Applications》1994,1(4):313-322
We consider a Lagrangian Differential System (L.D.S.) with Lagrangian function L(q,
)=T(q,
)+U(q), sufficiently smooth in a neighbourhood of the critical pointq=0 of the potential functionU(q). The kinetic function T(q,
) is a non homogeneous quadratic function of the
's, i.e. the L.D.S. contains the so-called gyroscopic forces. The potential functionU(q) starts with a degenerate (but non zero), semidefinite-negative, quadratic form. Moreover,q=0 is not a proper maximum ofU, and this property has to be recognized in a suitable way. By analizing the problem of the existence of solutions of the L.D.S., which asymptotically tend to the equilibrium solution, (q,
)=(0,0), we provide a sufficient criterium for its instability.Work performed under the auspices of M.U.R.S.T. (Ministero dell'Universitá e della Ricerca Scientifica e Tecnologica) and G.N.F.M. (Gruppo Nazionale di Fisica Matematica of the National Research Council (C.N.R.)). 相似文献
14.
Prof. Ottmar Loos 《Monatshefte für Mathematik》1978,86(2):107-129
Every Jordan pair
defines an algebraic varietyX containing
as a dense open subset.X is projective (affine) if and only if
is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of
. If
is separable then the automorphism group ofX is the projective group of
. 相似文献
15.
V. Bálint A. Bálintová M. Branická P. Grešák I. Hrinko P. Novotný M. Stacho 《Geometriae Dedicata》1993,46(2):173-180
We show that for any convex bodyKE
2 there exists a triangleT such that
, where T is a suitable homothetic copy ofT with ratio . As a corollary we show that if (K
i) are homothetic copies of a given convex bodyKE
2 with areaV(K)=1, then the condition
is sufficient for the existence of a translative covering ofK by (K
i). 相似文献
16.
Orazio Puglisi 《Geometriae Dedicata》1996,63(1):95-112
In this paper we describe the structure and the conjugacy classes of Sylow p-subgroups of FGL(V,
), the group of finitary
-automorphisms of the
-vector space V.The Author is member of the GNSAGA. 相似文献
17.
For 1/p+1/q1, we study the closed ideal
formed by the (c
o
,p,q)-summing operators. It turns out thatT:XY does not belong to
if and only if it factors the mapId:l
p
*l
q
. By localization, we get the ideal
that consists of those operatorsT for which all ultrapowersT
u
are contained in
. Operators in the complement of
are characterized by the property that they factor the mapsId:l
p
*n
l
q
n
uniformly. Our main tools are ideal norms.Supported by DFG grant PI 322/1-2 相似文献
18.
Atube of even orderq=2
d
is a setT={L,
} ofq+3 pairwise skew lines in PG(3,q) such that every plane onL meets the lines of
in a hyperoval. Thequadric tube is obtained as follows. Take a hyperbolic quadricQ=Q
3
+
(q) in PG(3,q); letL be an exterior line, and let
consist of the polar line ofL together with a regulus onQ.In this paper we show the existence of tubes of even order other than the quadric one, and we prove that the subgroup of PL(4,q) fixing a tube {L,
} cannot act transitively on
. As pointed out by a construction due to Pasini, this implies new results for the existence of flat .C
2 geometries whoseC
2-residues are nonclassical generalized quadrangles different from nets. We also give the results of some computations on the existence and uniqueness of tubes in PG(3,q) for smallq. Further, we define tubes for oddq (replacing hyperoval by conic in the definition), and consider briefly a related extremal problem.Dedicated to luigi antonio rosati on the occasion of his 70th birthday 相似文献
19.
Xu Cheng 《Bulletin of the Brazilian Mathematical Society》2000,31(2):225-239
We prove that a complete noncompact oriented strongly stable hypersurfaceM
n
with cmc (constant mean curvature)H in a complete oriented manifoldN
n+1
with bi-Ricci curvature, satisfying
alongM, admits no nontrivialL
2 harmonic 1-forms. This implies ifM
n
(2n4) is a complete noncompact strongly stable hypersurface in hyperbolic spaceH
n+1(–1) with cmc
, there exist no nontrivialL
2 harmonic 1-forms onM. We also classify complete oriented strongly stable surfaces with cmcH in a complete oriented manifoldN
3 with scalar curvature
satisfying
. 相似文献
20.
This paper deals with polarized pairs
, where
is a nonsingular projective threefold and
is a very ample line bundle on it, such that for one smooth member  |
|, one has (Â)=2. A large class of pairs whose adjoint line bundle is nef and big was indirectedly studied by Beltrametti and co-workers. We add some more information, both in this general case and also when the adjoint line bundle fails to be nef and big. 相似文献