On theta pairs for a maximal subgroup

For a maximal eubgroup M of a finite group G, a 8-pair is any pair of subgroups (C,D) of G such that (i) D?G, D≤C, (ii) - G, - M and (iii) C/D has no proper normal subgroup of G/D. A partial order may be defined on the family of 8-pairs. Let △(M) - {(C,D)|(C,D) is a maximal 8-pair and CM - G}. The purpose of this note is to prove: (1) A group G is solvable if and only if, for each maximal subgroup M of G, △(M) contains a 8-pair (C,D) such that C/D ie nilpctent. (2) If a group G is S₄-free, then G ia eupersolvable if and only if, for each maximal subgroup M of G, △(M) contains a 8-pair (C,D) auch that C/D is cyclic     

Some characterizations of magnetic Sobolev spaces

ABSTRACT

The aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions.     

Generating dual Baer modules via fully invariant submodules

Abstract

In this paper, we introduce a concept of a dual F-Baer module M where F is the fully invariant submodule of M, by this means we deal with generating dual Baer modules. We investigate direct sums of dual F -Baer modules M by exerting the notion of relatively dual F-Baer modules. We also obtain applications of dual F-Baer modules to rings and the preradical Z*(·).     

Abundance of stable ergodicity

We consider the set of volume preserving partially hyperbolic diffeomorphisms on a compact manifold having 1-dimensional center bundle. We show that the volume measure is ergodic, and even Bernoulli, for any C ² diffeomorphism in an open and dense subset of This solves a conjecture of Pugh and Shub, in this setting.     

The category of modules over a monoidal category: Abelian or not?

LetA be an algebra in an abelian monoidal category M. We prove that the category of leftA-modules is abelian, wheneverA is right coflat. This paper was written while the author was member of G.N.S.A.G.A. with partial financial support from M.I.U.R.     

Selection principles in hyperspaces with generalized Vietoris topologies

We continue investigations of ?ech closure spaces and their hyperspaces started in [M. Mrševi?, M. Jeli?, Selection principles and hyperspace topologies in closure spaces, J. Korean Math. Soc. 43 (2006) 1099-1114] and [M. Mrševi?, M. Jeli?, Selection principles, γ-sets and αi-properties in ?ech closure spaces, Topology Appl., in press], focusing on generalized upper and lower Vietoris topologies.     

Commutator length of symplectomorphisms

Each element $x$ of the commutator subgroup $[G, G]$ of a group $G$ can be represented as a product of commutators. The minimal number of factors in such a product is called the commutator length of $x$. The commutator length of $G$ is defined as the supremum of commutator lengths of elements of $[G, G]$. We show that for certain closed symplectic manifolds $(M,\omega)$, including complex projective spaces and Grassmannians, the universal cover $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ of the group of Hamiltonian symplectomorphisms of $(M,\omega)$ has infinite commutator length. In particular, we present explicit examples of elements in $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ that have arbitrarily large commutator length -- the estimate on their commutator length depends on the multiplicative structure of the quantum cohomology of $(M,\omega)$. By a different method we also show that in the case $c_1 (M) = 0$ the group $\widetilde{\hbox{\rm Ham}\, (M,\omega)$ and the universal cover ${\widetilde{\Symp}}_0\, (M,\omega)$ of the identity component of the group of symplectomorphisms of $(M,\omega)$ have infinite commutator length.     

Integration by parts formulas and dilatation vector fields on elliptic probability spaces

Summary. By coupling two arbitrary riemannian connections Γ and Γ˜ on a riemannian manifold M, we perform the stochastic calculus of ɛ-variation on the path space P(M) of the manifold M. The method uses direct calculations on Ito’s stochastic differential equations. In this context, we obtain intertwinning formulas with the Ito map for first order operators on the path space P(M) of M. By a judicious choice of the second connection Γ˜ in terms of the connection Γ, we can prolongate the intertwinning formulas to second order differential operators. Thus, we obtain expressions of heat operators on the path space P(M) of a riemannian manifold M endowed with an arbitrary connection. The integration by parts of the laplacians on P(M) leads us to the notion of dilatation vector field on the path space. Received: 18 April 1995 / In revised form: 18 March 1996     

Attached primes of the top local cohomology modules with respect to an ideal

Let be a Noetherian local ring and let be an ideal of R. Let M be an R-module of dimension n. In this paper we study the attached primes of the top local cohomology module Received: 12 May 2004     

Affine complete Stone algebras

In [1] R. Beazer characterized affine complete Stone algebras having a smallest dense element. We remove this latter assumption and describe affine complete algebras in the class of all Stone algebras.Dedicated to the memory of M. KolibiarPresented by Á. Szendrei.     

Starke Kotorsionsmoduln

Suppose that $(R, m)$ is a noetherian local ring and that E is the injective hull of the residue class field $R/m$. Suppose that M is an R-module, $M^0 = {\mbox{\rm Hom}}_R (M, E)$ is the Matlis dual of M and ${\mbox{\rm Coass}(M)} = {\mbox{\rm Ass} (M^0)}$. M is called cotorsion if every prime ideal ${\frak p} \in {\mbox{\rm Coass}}(M)$ is regular; it is called strongly cotorsion if $\cap {\rm Coass}(M)$ is regular. In the first part, we completely describe the structure of the strongly cotorsion modules over R, use this to determine the coassociated prime ideals of the bidual $M^{00}$, and give in the second part criteria for a cotorsion module being strongly cotorsion. Received: 7 March 2002     

A fast algorithm for the multivariate Birkhoff interpolation problem

Multivariate Birkhoff interpolation is the most complicated polynomial interpolation problem and the theory about it is far from systematic and complete. In this paper we derive an Algorithm B-MB (Birkhoff-Monomial Basis) and prove B-MB giving the minimal interpolation monomial basis w.r.t. the lexicographical order of the multivariate Birkhoff problem. This algorithm is the generalization of Algorithm MB in [L. Cerlinco, M. Mureddu, From algebraic sets to monomial linear bases by means of combinatorial algorithms, Discrete Math. 139 (1995) 73-87] which is a well known fast algorithm used to compute the interpolation monomial basis of the Hermite interpolation problem.     

Point-Free Version of Kakutani Duality

There are many results proved using the Axiom of Choice. Using point-free topology, we can prove some of these results without using this axiom. B. Banaschewski in [Pointfree Topology and the Spectra of f-rings, Ordered algebraic structures (Curacoa, 1995), Kluwer, Dordrecht, 123–148], studying the spectra of f-rings, describes the point-free version of the classical Gelfand duality without using the Axiom of Choice In this paper, referring to [Ebrahimi, M. M., Karimi Feizabadi, A. and Mahmoudi, M.: Pointfree Spectra of Riesz Space, Appl. Categ. Struct. 12 (2004), 397–409; Ebrahimi, M. M. and Karimi Feizabadi, A.: Pointfree Spectra of ℓ-Modules, To appear in J. Pure Appl. Algebra], we describe a point-free version of the classical Kakutani duality. For this, using one of the spectra given in [Ebrahimi, M. M., Karimi Feizabadi, A. and Mahmoudi, M.: Pointfree Spectra of Riesz Space, Appl. Categ. Struct. 12 (2004), 397–409; Ebrahimi, M. M. and Karimi Feizabadi, A.: Pointfree Spectra of l-Modules, To appear in J. Pure Appl. Algebra], we find an adjunction between the category of compact completely regular frames with frame maps and the category of Archimedean bounded Riesz spaces with continuous Riesz maps.     

A note on the discrete approximation of discontinuous curves and surfaces

This is a note on the paper [A. Kouibia, A.J. López-Linares, M. Pasadas, Approximation of discontinuous curves and surfaces with tangent conditions, J. Comput. Appl. Math. 193 (2006) 51–64]. We consider the constructing problem of a discontinuous parametric curve or surface from a finite set of points and tangent conditions. We develop a method based on the theory of discrete smoothing variational splines conveniently adapted to introduce the tangent conditions and the discontinuity set. We give a convergence result and we analyze some numerical and graphical examples in order to illustrate the effectiveness of the presented method.     

Differential equations on variable time scales

We introduce a class of differential equations on variable   time scales with a transition condition between two consecutive parts of the scale. Conditions for existence and uniqueness of solutions are obtained. Periodicity, boundedness and stability of solutions are considered. The method of investigation is by means of two successive reductions: B$B$-equivalence of the system [E. Akalín, M.U. Akhmet, The principles of B-smooth discontinuous flows, Computers and Mathematics with Applications 49 (2005) 981–995; M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163–178; M.U. Akhmet, N.A. Perestyuk, The comparison method for differential equations with impulse action, Differential Equations 26 (9) (1990) 1079–1086] on a variable time scale to a system on a time scale, a reduction to an impulsive differential equation [M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163–178; M.U. Akhmet, M. Turan, The differential equations on time scales through impulsive differential equations, Nonlinear Analysis 65 (2006) 2043–2060]. Appropriate examples are constructed to illustrate the theory.     

Judicious partitions of graphs

To 80^th birthday of Paul Erds     

The existence of large commutator subgroups in factors and subgroups of non-nilpotent groups

We prove that any finite non-nilpotent group G must possess certain factors K / M with a large commutator subgroup, where M is nilpotent. These results are related to recent results by M. Herzog and the authors on large commutator subgroups.Received: 26 August 2004     

T0-SEPARATION IN TOPOLOGICAL CATEGORIES

R.-E. Hoffmann [5,6] has introduced the notion of an (E,M)-universally topological functor, which provides a categorical characterization of the T₀-separation axiom of general topology. In this paper, we characterise these functors in terms of the unique extension of structure functors defined on the subcategory of “separated” objects (of the domain category). This, in turn, leads to a solution of some problems due to G.C.L. Brümmer [1,2]. Other results include a generalization of L. Skula's characterization of the bireflective subcategories of Top [10].     

A large set containing few orbits of measure preserving transformations

Summary There exists a Borel set C of product Lebesgue measure one in the Hilbert cube having the property that, for every measure preserving transformationT of the unit interval, allT-orbits contained inC originate from a zero set. This settles an infinite dimensional version of a problem raised by Th. M. Rassias.