scholarly journals Random generalized functions of locally finite order

1968 ◽  
Vol 19 (6) ◽  
pp. 1457-1457 ◽  
Author(s):  
D. M. Eaves
Keyword(s):  
Finite Order ◽  
Generalized Functions ◽  
Locally Finite

Stretchings

1996 ◽  
Vol 61 (2) ◽  
pp. 563-585 ◽  
Author(s):  
O. Finkel ◽  
J. P. Ressayre
Keyword(s):  
Finite Order ◽  
Order Type ◽  
Finitely Generated ◽  
Locally Finite ◽  
Mahlo Cardinals

AbstractA structure is locally finite if every finitely generated substructure is finite; local sentences are universal sentences all models of which are locally finite. The stretching theorem for local sentences expresses a remarkable reflection phenomenon between the finite and the infinite models of local sentences. This result in part requires strong axioms to be proved; it was studied by the second named author, in a paper of this Journal, volume 53. Here we correct and extend this paper; in particular we show that the stretching theorem implies the existence of inaccessible cardinals, and has precisely the consistency strength of Mahlo cardinals of finite order. And we present a sequel due to the first named author:(i) decidability of the spectrum Sp(φ) of a local sentence φ, below ωω; where Sp(φ) is the set of ordinals α such that φ has a model of order type α(ii) proof that bethω = sup{Sp(φ): φ local sentence with a bounded spectrum}(iii) existence of a local sentence φ such that Sp(φ) contains all infinite ordinals except the inaccessible cardinals.

A characteristically simple group

1954 ◽  
Vol 50 (4) ◽  
pp. 641-642 ◽  
Author(s):  
D. H. McLain
Keyword(s):  
Simple Group ◽  
Finite Order ◽  
Commutator Subgroup ◽  
Unit Group ◽  
Characteristic Subgroup ◽  
Normal Subgroups ◽  
Locally Finite ◽  
Finite Set ◽  
Group A ◽  
Trivial Centre

The object of this note is to give an example of an infinite locally finite p-group which has no proper characteristic subgroup except the unit group. (A group G is a locally finite p-group if every finite set of elements of G generates a subgroup of finite order equal to a power of the prime p.) It is known that an infinite locally finite p-group cannot be simple, for if it were it would satisfy the minimal condition for normal subgroups, and so have a non-trivial centre (see(1)). However our example shows that it can be characteristically-simple. Examples are known of locally finite p-groups with trivial centre ((2), (4)), and of locally finite p-groups coinciding with their commutator groups ((1), (5)). Since the centre and commutator subgroup of a group are characteristic subgroups our example will have both of these properties. We may remark that the direct product of a simple, or even of a characteristically-simple group with itself any number of times is also characteristically-simple, but by Corollary 2.1 our group cannot be so decomposed.

scholarly journals On profinite groups in which commutators are Engel

2001 ◽  
Vol 70 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Pavel Shumyatsky
Keyword(s):  
Finite Order ◽  
Profinite Group ◽  
Profinite Groups ◽  
Finitely Generated ◽  
Locally Finite ◽  
Locally Nilpotent ◽  
Additional Assumptions

AbstractWe show that if G is a finitely generated profinite group such that [x1, x2, …, xk] is Engel for any x1, x2, …, xk ∈ G, then γ(G) is locally nilpotent, and if [x1, x2, …, xk] has finite order for any x1, x2, …, xk ∈ G then, under some additional assumptions, γk(G) is locally finite.

scholarly journals MULTISCALE MODELLING AND COMPUTATION OF MICROSTRUCTURES IN MULTI-WELL PROBLEMS

2004 ◽  
Vol 14 (09) ◽  
pp. 1343-1360 ◽  
Author(s):  
ZHIPING LI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Order ◽  
Numerical Experiments ◽  
Large Deformations ◽  
Multiscale Model ◽  
Inhomogeneous Deformation ◽  
The Finite Element Method ◽  
Locally Finite ◽  
Rank One

A multiscale model and numerical method for computing microstructures with large and inhomogeneous deformation is established, in which the microscopic and macroscopic information is recovered by coupling the finite order rank-one convex envelope and the finite element method. The method is capable of computing microstructures which are locally finite order laminates. Numerical experiments on a double-well problem show that plenty of stress free large deformations can be achieved by microstructures consisting of piecewise simple twin laminates.

Automorphisms of finite order of nilpotent groups II

2014 ◽  
Vol 51 (4) ◽  
pp. 547-555 ◽  
Author(s):  
B. Wehrfritz
Keyword(s):  
Nilpotent Group ◽  
Finite Order ◽  
Finite Index ◽  
Nilpotent Groups ◽  
Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

Finite-order Integration Weights Can be Dangerous

2007 ◽  
Vol 7 (3) ◽  
pp. 239-254 ◽  
Author(s):  
I.H. Sloan
Keyword(s):  
Function Space ◽  
Finite Order ◽  
Small Subset ◽  
Worst Case ◽  
Integration Rule ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Sum Of Functions ◽  
Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

On Commutation Properties of the Composition Relation of Convergent and Divergent Permutations (Part I)

2014 ◽  
Vol 58 (1) ◽  
pp. 13-22
Author(s):  
Roman Wituła ◽  
Edyta Hetmaniok ◽  
Damian Słota
Keyword(s):  
Finite Order ◽  
Convergent Series ◽  
The Other ◽  
Other Hand ◽  
The Family ◽  
Composition Relation ◽  
The Continuum

Abstract In the paper we present the selected properties of composition relation of the convergent and divergent permutations connected with commutation. We note that a permutation on ℕ is called the convergent permutation if for each convergent series ∑an of real terms, the p-rearranged series ∑ap(n) is also convergent. All the other permutations on ℕ are called the divergent permutations. We have proven, among others, that, for many permutations p on ℕ, the family of divergent permutations q on ℕ commuting with p possesses cardinality of the continuum. For example, the permutations p on ℕ having finite order possess this property. On the other hand, an example of a convergent permutation which commutes only with some convergent permutations is also presented.

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