Search results for "Abelian group"
showing 10 items of 160 documents
Darboux systems with a cusp point and pseudo-abelian integrals
2018
International audience; We study pseudo-abelian integrals associated with polynomial deformations of Darboux systems having a cuspidal singularity. Under some genericity hypothesis we provide locally uniform boundedness of on the number of their zeros.
Rotation Forms and Local Hamiltonian Monodromy
2017
International audience; The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a general approach to the computation of monodromy that resembles the analytical one, reducing the problem to the computation of residues of polar 1-forms. We apply our technique to three celebrated examples of systems with monodromy (the champagne bottle, the spherical pendulum, the hydrogen atom) and to the case of non-degenerate focus-focus singularities, re-obtaining the classical results. An advantage of this approach …
On the classification of CAT(0) structures for the 4-string braid group
2005
This paper is concerned with the class of so-called CAT(0) groups, namely, those groups that admit a geometric (i.e., properly discontinuous, co-compact, and isometric) action on some CAT(0) space. More precisely, we are interested in knowing to what extent it is feasible to classify the geometric CAT(0) actions of a given group (up to, say, equivariant homothety of the space). A notable example of such a classification is the flat torus theorem, which implies that the minimal geometric CAT(0) actions of the free abelian group Z (n ≥ 1) are precisely the free actions by translations of Euclidean space E. Typically, however, a given group will have uncountably many nonequivalent actions, mak…
$MC$-hypercentral groups
2007
This paper is devoted to the imposition of some chain conditions on groups having a generalized central series. It is also given a characterization of MC-groups with finite abelian section rank: such class of groups is a suitable enlargement of the class of FC-groups. Mathematics Subject Classification: 20F24; 20F14
Group Identities on Units of Group Algebras
2000
Abstract Let U be the group of units of the group algebra FG of a group G over a field F . Suppose that either F is infinite or G has an element of infinite order. We characterize groups G so that U satisfies a group identity. Under the assumption that G modulo the torsion elements is nilpotent this gives a complete classification of such groups. For torsion groups this problem has already been settled in recent years.
Some new (s,k,?)-translation transversal designs with non-abelian translation group
1989
For λ >1 and many values of s andk, we give a construction of (s,k,λ)-partitions of finite non-abelian p-groups and of Frobenius groups with non-abelian kernel. These groups are associated with translation transversl designs of the same parameters.
Abelian Sylow subgroups in a finite group, II
2015
Abstract Let p ≠ 3 , 5 be a prime. We prove that Sylow p-subgroups of a finite group G are abelian if and only if the class sizes of the p-elements of G are all coprime to p. This gives a solution to a problem posed by R. Brauer in 1956 (for p ≠ 3 , 5 ).
The Abelian Kernel of an Inverse Semigroup
2020
The problem of computing the abelian kernel of a finite semigroup was first solved by Delgado describing an algorithm that decides whether a given element of a finite semigroup S belongs to the abelian kernel. Steinberg extended the result for any variety of abelian groups with decidable membership. In this paper, we used a completely different approach to complete these results by giving an exact description of the abelian kernel of an inverse semigroup. An abelian group that gives this abelian kernel was also constructed.
Abelian Integrals: From the Tangential 16th Hilbert Problem to the Spherical Pendulum
2016
In this chapter we deal with abelian integrals. They play a key role in the infinitesimal version of the 16th Hilbert problem. Recall that 16th Hilbert problem and its ramifications is one of the principal research subject of Christiane Rousseau and of the first author. We recall briefly the definition and explain the role of abelian integrals in 16th Hilbert problem. We also give a simple well-known proof of a property of abelian integrals. The reason for presenting it here is that it serves as a model for more complicated and more original treatment of abelian integrals in the study of Hamiltonian monodromy of fully integrable systems, which is the main subject of this chapter. We treat i…
Polaroid-Type Operators
2018
In this chapter we introduce the classes of polaroid-type operators, i.e., those operators T ∈ L(X) for which the isolated points of the spectrum σ(T) are poles of the resolvent, or the isolated points of the approximate point spectrum σap(T) are left poles of the resolvent. We also consider the class of all hereditarily polaroid operators, i.e., those operators T ∈ L(X) for which all the restrictions to closed invariant subspaces are polaroid. The class of polaroid operators, as well as the class of hereditarily polaroid operators, is very large. We shall see that every generalized scalar operator is hereditarily polaroid, and this implies that many classes of operators acting on Hilbert s…