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1.
Let G be a finite group,
a normal subgroup, p a prime,
a finite splitting field of characteristic p for
G and
We prove that
is a splitting field for N, using the action
of the Galois group of the field extension
on the irreducible representations of N.
As
is a splitting field for the symmetric group
Sn
we get as a corollary that
is a splitting field for the alternating group
An.
Received: 31 July 2003 相似文献
2.
S. Zhang 《Algebra Universalis》1996,35(4):485-505
Let
be a variety of completely regular semigroups. Define
C
* to be the class of all completely regular semigroupsS whose least full and self-conjugate subsemigroupC
*(S) belongs to
. ThenC
* is an operator on the lattice
of varieties of completely regular semigroups. In this note we show that the order ofC
* is infinite. This fact yields that the Mal'cev project is not associative on
. We describe
(C
*)1,
andi 0, in terms of -invariant normal subgroups of the free group over a countably infinite set. The lattice theoretic properties ofC
* are also studied.Presented by W. Taylor. 相似文献
3.
4.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献
5.
In the metastable range, a class of mappings yielding a negative solution of the isotopic realization problem (posed by E. V. Shchepin in 1993) and satisfying an additional technical condition is described in algebraic terms. Namely, one constructs an obstruction to isotopic realization of a discretely realizable continuous mapping f of an n-polyhedron to an orientable PL m-manifold; the completeness of this obstruction is established for
in the case where f is discretely realizable by skeleta. Also, for
, a series of mappings
(with singular set consisting of a p-adic solenoid,
, and a point) is presented for which the problem is solved in the negative. Furthermore, it is shown that the problem is solved in the affirmative in the metastable range if stabilization with codimension one is allowed, as well as in the case of a mapping
, under the condition that f is discretely realizable by skeleta and the configuration singular set
is acyclic in dimension
(in the sense of the SteenrodSitnikov homology). Bibliography: 31 titles. 相似文献
6.
Let A(X) be the space defined by Waldhausen whose homotopy groups define the algebraic K-groups of the space X and let
. Here (X) denotes the free loop space of X and Q denotes the functor . For X = Y, the suspension of a connected space Y, we shall prove that the homotopy fibers Ã(X), B(X) of the maps A(X) A (point), B(X) B (point) are equivalent as infinite loop spaces. 相似文献
7.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
8.
Introduce the notation:
, is the union of two segments [-1,1] and [-1 +
,1+
],
is a noninteger number,
is the Hölder class with exponent
on
The following result announced by the authors in [J. Math. Sci. 117 (2003), No. 3] is proved. There exist numbers a
1 (
) , b
1 (
)
0 depending only on
such that for any
there exists a polynomial
, such that
. Bibliography: 11 titles. 相似文献
9.
Horst Elmar Winkelnkemper 《Annals of Global Analysis and Geometry》1992,10(3):209-218
Let
t
be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M
n
, whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d
t
and, for each x M, we define a smooth real function
x
(t) : (1 +
i
(t)), where the i(t) are the eigenvalues of AA
T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t
, restricted to v at the point x
-t M
n.Among other things, we prove the
Theorem (Theorem II, below). Assume v is also volume preserving and that
x
'
(t) 0 for all x M and real t; then, if
x
t
: M M is weakly missng for some t, it is necessary that vx 0 at all x M. 相似文献
10.
Patrick Headley 《Journal of Algebraic Combinatorics》1997,6(4):331-338
Let be an irreducible crystallographic rootsystem in a Euclidean space V, with + theset of positive roots. For ,
, let
be the hyperplane
. We define a set of hyperplanes
. This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincaré polynomial of
is
, where n is the rank of and h is the Coxeter number of the finiteCoxeter group corresponding to . 相似文献
11.
Arlene A. Pascasio Cheryl E. Praeger Blessilda P. Raposa 《Designs, Codes and Cryptography》1996,8(1-2):173-179
We show that a non-symmetric nearly triply regular
designD with
and in which every line has at least q points is AG(n,q) for prime power q > 2 and positiveinteger n 3. 相似文献
12.
Mervyn J. Silvapulle Pranab K. Sen 《Annals of the Institute of Statistical Mathematics》1993,45(1):159-171
Consider the linear modelY=X+E in the usual matrix notation where the errors are independent and identically distributed. We develop robust tests for a large class of one- and two-sided hypotheses about when the data are obtained and tests are carried out according to a group sequential design. To illustrate the nature of the main results, let
and
be anM- and the least squares estimator of respectively which are asymptotically normal about with covariance matrices 2(X
t
X)–1 and 2(X
t
X)–1 respectively. Let the Wald-type statistics based on
and
be denoted byRW andW respectively. It is shown thatRW andW have the same asymptotic null distributions; here the limit is taken with the number of groups fixed but the numbers of observations in the groups increase proportionately. Our main result is that the asymptotic Pitman efficiency ofRW relative toW is (2/2). Thus, the asymptotic efficiency-robustness properties of
relative to
translate to asymptotic power-robustness ofRW relative toW. Clearly, this is an attractive result since we already have a large literature which shows that
is efficiency-robust compared to
. The results of a simulation study show that with realistic sample sizes,RW is likely to have almost as much power asW for normal errors, and substantially more power if the errors have long tails. The simulation results also illustrate the advantages of group sequential designs compared to a fixed sample design, in terms of sample size requirements to achieve a specified power. 相似文献
13.
We express the real connective K-theory groups
o4k–1(B
Q
) ofthe quaternion group Q
of order = 2
j
8 in terms of therepresentation theory of Q
by showing
o4k–1(B
Q
) =
Sp(S
4k+3/Q
)where is any fixed point free representation of Q
in U(2k + 2). 相似文献
14.
Micheline Vigué-Poirrier 《manuscripta mathematica》1986,56(2):177-191
Let X be a nilpotent space such that it exists k1 with Hp (X,) = 0 p > k and Hk (X,) 0, let Y be a (m–1)-connected space with mk+2, then the rational homotopy Lie algebra of YX (resp.
is isomorphic as Lie algebra, to H* (X,) (* (Y) ) (resp.+ (X,) (* (Y) )). If X is formal and Y -formal, then the spaces YX and
are -formal. Furthermore, if dim * (Y) is infinite and dim H* (Y,Q) is finite, then the sequence of Betti numbers of
grows exponentially. 相似文献
15.
Siegfried Steiner 《manuscripta mathematica》1977,20(3):277-300
Let E be a n-dimensional euclidean vector space. The subset V
k
n
={x ... x | x E} of kE is called a Veronesemanifold. The scalar product of E induces a euclidean structure on kE. Passing to the corresponding projective space
, one may consider
as a riemannian submanifold of the space form
. In this paper we study properties of the pair
of riemannian manifolds. 相似文献
16.
Ján Jakubík 《Czechoslovak Mathematical Journal》2002,52(3):651-663
Let Int
be the lattice of all intervals of an MV-algebra
. In the present paper we investigate the relations between direct product decompositions of
and (i) the lattice Int
, or (ii) 2-periodic isometries on
, respectively. 相似文献
17.
On the Harris Recurrence of Iterated Random Lipschitz Functions and Related Convergence Rate Results 总被引:1,自引:0,他引:1
Gerold Alsmeyer 《Journal of Theoretical Probability》2003,16(1):217-247
A result by Elton(6) states that an iterated function system
of i.i.d. random Lipschitz maps F
1,F
2,... on a locally compact, complete separable metric space
converges weakly to its unique stationary distribution if the pertinent Liapunov exponent is a.s. negative and
for some
. Diaconis and Freedman(5) showed the convergence rate be geometric in the Prokhorov metric if
for some p>0, where L
1 denotes the Lipschitz constant of F
1. The same and also polynomial rates have been recently obtained in Alsmeyer and Fuh(1) by different methods. In this article, necessary and sufficient conditions are given for the positive Harris recurrence of (M
n
)
n0 on some absorbing subset
. If
and the support of has nonempty interior, we further show that the same respective moment conditions ensuring the weak convergence rate results mentioned above now lead to polynomial, respectively geometric rate results for the convergence to in total variation or f-norm
f
, f(x)=1+d(x,x
0)
for some (0,p]. The results are applied to various examples that have been discussed in the literature, including the Beta walk, multivariate ARMA models and matrix recursions. 相似文献
18.
Majorants and Extreme Points of Unit Balls in Bernstein Spaces 总被引:1,自引:1,他引:0
The Bernstein space B
p () (1
$$
" align="middle" border="0">
0) is the set of functions from L
p(
) having Fourier transforms (in the sense of generalized functions) with supports in the compact segment [- , ]. Every function f
has an analytic continuation onto the complex plane, which is an entire function of exponential type . The spaces B
p ()\, are conjugate Banach spaces. Therefore, the closed unit ball
in B
p () has a rich set of extreme (boundary) points:
coincides with the weakly * closed convex hull of its extreme points. Since, for 1< p< , B
p () is a uniformly convex space, only the balls
and
have nontrivially arranged sets of extreme points. In this paper, in terms of zeros of entire functions, we obtain necessary and sufficient conditions of extremeness for functions from
. 相似文献
19.
We prove four theorems about groups with a dihedral (or cyclic) image containing a difference set. For the first two, suppose G, a group of order 2p
with p an odd prime, contains a nontrivial (v, k, ) difference set D with order n = k – prime to p and self-conjugate modulo p. If G has an image of order p, then 0 2a +
2
for a unique choice of = ±1, and for a = (k –
)/2p. If G has an image of order 2p, then
and
(
– 1)/(
– 1). There are further constraints on n, a and . We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, ) difference set D and has a dihedral image D
2m
with either (n, m) = 1 or m = p
t
for p an odd prime dividing n, then one of the C
2 intersection numbers of D is divisible by m. Again, this gives some non-existence results. 相似文献
20.
Marian Nowak 《Czechoslovak Mathematical Journal》2000,50(2):401-414
Let
be a real Banach space and let E be an ideal of L
0 over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function
, defined by
, belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology
the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. 相似文献