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1.
2.
Let be a nonstandard model of Peano Arithmetic with domain M and let be nonstandard. We study the symmetric and alternating groups S
n
and A
n
of permutations of the set internal to , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide
evidence that A
n
and S
n
are not split extensions by these normal subgroups, by showing that any such complement if it exists, cannot be a limit of
definable sets. We conclude by identifying an -valued metric on and (where B
S
, B
A
are the maximal normal subgroups of S
n
and A
n
identified earlier) making these groups into topological groups, and by showing that if is -saturated then and are complete with respect to this metric.
相似文献
3.
Alexander A. Ivanov 《Journal of Algebraic Combinatorics》1992,1(1):45-69
The sporadic simple group F
2 known as Fischer's Baby Monster acts flag-transitively on a rank 5 P-geometry
. P-geometries are geometries with string diagrams, all of whose nonempty edges except one are projective planes of order 2 and one terminal edge is the geometry of the Petersen graph. Let
be a flag-transitive P-geometry of rank 5. Suppose that each proper residue of
is isomorphic to the corresponding residue in
. We show that in this case
is isomorphic to
. This result realizes a step in classification of the flag-transitive P-geometries and also plays an important role in the characterization of the Fischer–Griess Monster in terms of its 2-local parabolic geometry. 相似文献
4.
We classify the quadratic extensions and the finite groups G for which the group ring [G] of G over the ring of integers of K has the property that the group of units of augmentation 1 is hyperbolic. We also construct units in the ℤ-order of the quaternion algebra , when it is a division algebra. 相似文献
5.
Shripad M. Garge 《Proceedings Mathematical Sciences》2005,115(4):411-427
The aim of this paper is to investigate the order coincidences among the finite semisimple groups and to give a reasoning
of such order coincidences through the transitive actions of compact Lie groups.
It is a theorem of Artin and Tits that a finite simple group is determined by its order, with the exception of the groups
(A3(2), A2(4)) and(B
n
(q), C
n
(q)) forn ≥ 3,q odd. We investigate the situation for finite semisimple groups of Lie type. It turns out that the order of the finite
group H(
) for a split semisimple algebraic groupH defined over
, does not determine the groupH up to isomorphism, but it determines the field
under some mild conditions. We then put a group structure on the pairs(H
1,H
2) of split semisimple groups defined over a fixed field
such that the orders of the finite groups H1(
) and H2(
) are the same and the groupsH
i
have no common simple direct factors. We obtain an explicit set of generators for this abelian, torsion-free group. We finally
show that the order coincidences for some of these generators can be understood by the inclusions of transitive actions of
compact Lie groups. 相似文献
6.
Luis Javier Hernández Paricio 《Applied Categorical Structures》2005,13(5-6):421-451
For each n > 1 and each multiplicative closed set of integers S, we study closed model category structures on the pointed category of topological spaces, where the classes of weak equivalences
are classes of maps inducing isomorphism on homotopy groups with coefficients in determined torsion abelian groups, in degrees
higher than or equal to n. We take coefficients either on all the cyclic groups with s ∈ S, or in the abelian group where is the group of fractions of the form with s ∈ S. In the first case, for n > 1 the localized category is equivalent to the ordinary homotopy category of (n − 1)-connected CW-complexes whose homotopy groups are S-torsion. In the second case, for n > 1 we obtain that the localized category is equivalent to the ordinary homotopy category of (n − 1)-connected CW-complexes whose homotopy groups are S-torsion and the nth homotopy group is divisible. These equivalences of categories are given by colocalizations , obtained by cofibrant approximations on the model structures. These colocalization maps have nice universal properties. For
instance, the map is final (in the homotopy category) among all the maps of the form Y → X with Y an (n − 1)-connected CW-complex whose homotopy groups are S-torsion and its nth homotopy group is divisible. The spaces , are constructed using the cones of Moore spaces of the form M(T, k), where T is a coefficient group of the corresponding structure of models, and homotopy colimits indexed by a suitable ordinal. If
S is generated by a set P of primes and S
p
is generated by a prime p ∈ P one has that for n > 1 the category is equivalent to the product category . If the multiplicative system S is generated by a finite set of primes, then localized category is equivalent to the homotopy category of n-connected Ext-S-complete CW-complexes and a similar result is obtained for . 相似文献
7.
We consider a real analytic foliation of by complex analytic manifolds of dimension m issued transversally from a CR generic submanifold of codimension m. We prove that a continuous CR function f on M which has separate holomorphic extension along each leaf, is holomorphic. When the leaves are cartesian straight planes,
separate holomorphic extension along suitable selections of these planes suffices and f turns out to be holomorphic in a neighbourhood of their union. If M is a hypersurface we can also specify the side of the extension, regardless the leaves are straight or not. 相似文献
8.
Let M be a right R-module,
the class of all M-small modules, and P a projective cover of M in
[M]. We consider the torsion theories
= (
),
= (
), and
= (
) in
[M], where
is the torsion theory generated by
is the torsion theory cogenerated by
, and
is the dual Lambek torsion theory. We study some conditions for
to be cohereditary, stable, or split, and prove that Rej(M,
) = M
=
(=
=
)
=
GenM(P)
.2000 Mathematics Subject Classification: 16S90 相似文献
9.
Henri Anciaux 《Geometriae Dedicata》2006,120(1):37-48
We give new examples of self-shrinking and self-expanding Lagrangian solutions to the Mean Curvature Flow (MCF). These are Lagrangian submanifolds in
, which are foliated by (n − 1)-spheres (or more generally by minimal (n − 1)-Legendrian submanifolds of
), and for which the study of the self-similar equation reduces to solving a non-linear Ordinary Differential Equation (ODE). In the self-shrinking case, we get a family of submanifolds generalising in some sense the self-shrinking curves found by Abresch and Langer. 相似文献
10.
Let G be a finite abelian group and S =
a minimal zero-sum sequence in G of maximal length |S| = l. We study the order of the elements
相似文献
11.
Jean B. Lasserre 《Mathematical Programming》2009,120(2):457-477
We provide a sufficient condition on a class of compact basic semialgebraic sets for their convex hull co(K) to have a semidefinite representation (SDr). This SDr is explicitly expressed in terms of the polynomials g
j
that define K. Examples are provided. We also provide an approximate SDr; that is, for every fixed , there is a convex set such that (where B is the unit ball of ), and has an explicit SDr in terms of the g
j
’s. For convex and compact basic semi-algebraic sets K defined by concave polynomials, we provide a simpler explicit SDr when the nonnegative Lagrangian L
f
associated with K and any linear is a sum of squares. We also provide an approximate SDr specific to the convex case.
相似文献
12.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
13.
Octavian G. Mustafa 《Annali di Matematica Pura ed Applicata》2008,187(2):187-196
Via an integral transformation, we establish two embedding results between the Emden-Fowler type equation , t ≥ t
0 > 0, with solutions x such that as , , and the equation , u > 0, with solutions y such that for given k > 0. The conclusions of our investigation are used to derive conditions for the existence of radial solutions to the elliptic
equation , , that blow up as in the two dimensional case.
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14.
Bang-Yen Chen 《Archiv der Mathematik》2008,91(4):366-371
Flat Lagrangian minimal surfaces in the Lorentzian complex plane are classified by B. Y. Chen and L. Vrancken in [8]. On the other hand, Vrancken proves in [11] that Lagrangian minimal surfaces
of constant curvature in are flat surfaces. In this article, we classify all Lagrangian minimal surfaces in which are free from flat points.
Received: 16 December 2007 相似文献
15.
M. I. Anokhin 《Mathematical Notes》1997,61(1):3-8
LetF be a free group with at most countable system
of free generators, letR be its normal subgroup recursively enumerable with respect to
, and let
be a variety of groups that differs from
and for which the corresponding verbal subgroupV of the free group of countable rank is recursive. It is proved that the word problem inF/V(R) is solvable if and only if this problem is solvable inF/R, and if
, then there exists anR such, that the conjugacy problem inF/R is solvable, but this problem is unsolvable inF/V(R) for any Abelian variety
(all algorithmic problems are regarded with respect to the images of
under the corresponding natural epimorphisms).
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 3–9, January, 1997.
Translated by M. I. Anokhin 相似文献
16.
Florent Schaffhauser 《Mathematische Annalen》2008,342(2):405-447
The importance of explicit examples of Lagrangian submanifolds of moduli spaces is revealed by papers such as Dostoglou and Salamon (Ann. of Math (2), 139(3), 581–640, 1994) and Salamon (Proceedings of the international congress of mathematicians, vol.1, 2 (Zürich, 1994), pp. 526–536. Birkhäuser, Basel, 1995): given a 3-manifold M with boundary ?M = Σ, Dostoglou and Salamon use such examples to obtain a proof of the Atiyah-Floer conjecture relating the symplectic Floer homology of the representation space Hom(π1(Σ = ?M), U)/U (associated to an explicit pair of Lagrangian submanifolds of this representation space) and the instanton homology of the 3-manifold M. In the present paper, we construct a Lagrangian submanifold of the space of representations ${\mathcal{M}_{g,l}:=Hom_\mathcal{C}(\pi_{g,l}, U)/U}The importance of explicit examples of Lagrangian submanifolds of moduli spaces is revealed by papers such as Dostoglou and
Salamon (Ann. of Math (2), 139(3), 581–640, 1994) and Salamon (Proceedings of the international congress of mathematicians,
vol.1, 2 (Zürich, 1994), pp. 526–536. Birkh?user, Basel, 1995): given a 3-manifold M with boundary ∂M = Σ, Dostoglou and Salamon use such examples to obtain a proof of the Atiyah-Floer conjecture relating the symplectic Floer
homology of the representation space Hom(π1(Σ = ∂M), U)/U (associated to an explicit pair of Lagrangian submanifolds of this representation space) and the instanton homology of the
3-manifold M. In the present paper, we construct a Lagrangian submanifold of the space of representations of the fundamental group π
g,l
of a punctured Riemann surface Σ
g,l
into an arbitrary compact connected Lie group U. This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on . We show that the involution is induced by a form-reversing involution β defined on the quasi-Hamiltonian space . The fact that has a non-empty fixed-point set is a consequence of the real convexity theorem for group-valued momentum maps proved in Schaffhauser
(A real convexity theorem for quasi-Hamiltonian actions, submitted, 25 p, 2007. ). The notion of decomposable representation provides a geometric interpretation of the Lagrangian submanifold thus obtained.
Supported by the Japanese Society for Promotion of Science (JSPS). 相似文献
17.
Maria Manfredini 《Annali di Matematica Pura ed Applicata》2009,188(3):417-428
In this paper we are concerned with a family of elliptic operators represented as sum of square vector fields: in , where Δ is the Laplace operator, m < n, and the limit operator is hypoelliptic. Here we establish Schauder’s estimates, uniform with respect to the parameter ϵ, of solution of the approximated
equation L
ϵ
u = f, using a modification of the lifting technique of Rothschild and Stein. These estimates can be used in particular while studying
regularity of viscosity solutions of nonlinear equations represented in terms of vector fields.
相似文献
18.
Let denote the set of even integers . We prove that when H ≥ X
0.33, almost all integers can be represented as the sum of a prime and the square of a prime. We also prove a similar result for sums of three squares
of primes.
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19.
Volodymyr Nekrashevych 《Geometriae Dedicata》2007,124(1):153-190
We construct and study a family of 3-generated groups parametrized by infinite binary sequences w. We show that two groups of the family are isomorphic if and only if the sequences are cofinal and that two groups cannot
be distinguished by finite sets of relations. We show a connection of the family with 2-dimensional holomorphic dynamics.
相似文献
20.
We prove the following statement.
Let , and let . Suppose that, for all and , the sequence satisfies the relation
where e(u) : = e2πiu
.
Then
where
q is the set of q-multiplicative functions g such that . 相似文献