A construction of superstable ndop-notop groups

1991 ◽  
Vol 56 (4) ◽  
pp. 1385-1390 ◽  
Author(s):  
Andreas Baudisch
Keyword(s):  
Nilpotent Group ◽  
Planar Graphs ◽  
Strong Form ◽  
Complete Theory ◽  
Primary Model ◽  
Elementary Submodel

AbstractThe paper continues [1]. Let S be a complete theory of ultraflat (e.g. planar) graphs as introduced in [4]. We show a strong form of NOTOP for S: The union of two models M1 and M2, independent over a common elementary submodel M0, is the primary model over M1 ∪ M2 of S. Then by results of [1] Mekler's construction [6] gives for such a theory S of nice ultraflat graphs a superstable 2-step-nilpotent group of exponent p (> 2) with NDOP and NOTOP.

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.

Acute Constraints in Straight-Line Drawings of Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 994-1001
Author(s):  
Akane SETO ◽  
Aleksandar SHURBEVSKI ◽  
Hiroshi NAGAMOCHI ◽  
Peter EADES
Keyword(s):  
Planar Graphs ◽  
Line Drawings ◽  
Straight Line

A Space-Efficient Separator Algorithm for Planar Graphs

2019 ◽  
Vol E102.A (9) ◽  
pp. 1007-1016 ◽  
Author(s):  
Ryo ASHIDA ◽  
Sebastian KUHNERT ◽  
Osamu WATANABE
Keyword(s):  
Planar Graphs

Saussurelaisen kielikäsityksen kritiikki

Virittäjä ◽  
2020 ◽  
Vol 124 (1) ◽  
Author(s):  
Mikko Laasanen
Keyword(s):  
Communication System ◽  
Written Language ◽  
Strong Form ◽  
Continuous Speech ◽  
Language Bias ◽  
Context Free ◽  
Ontological Concept

Artikkeli käsittelee saussurelaista kielikäsitystä kohtaan esitettyä kritiikkiä. Artikkelin tavoitteena on puolustaa saussurelaista kielikäsitystä ja esittää Saussure moni-puolisempana ajattelijana kuin mitä Kurssin vahvasti strukturalisesta luennasta voisi päätellä. Artikkelissa tarkastellaan käsitystä kielestä järjestelmänä (Saussuren langue), kontekstivapaata merkitystä, kirjoitetun kielen vääristymää (written language bias), Roy Harrisin kielimyyttiä sekä kielen dynaamisuutta. Artikkelissa esitetään, että langue on sekä metodologinen että ontologinen käsite, joka viittaa sekä kielen järjestäytymättömiin sääntöihin että kielitieteilijän niistä luomaan järjestelmään. Kontekstivapaan merkityksen osalta korostetaan sitä, että jonkinlainen merkityksen pysyvyys on välttämätön osa kieltä kommunikaatiojärjestelmänä. Artikkelissa argumentoidaan kirjoitetun kielen vääristymän vahvaa muotoa vastaan, jonka mukaan esimerkiksi puheen analysoiminen diskreeteiksi yksiköiksi johtuu kirjoitetun kielen vaikutuksesta. Harrisin kielimyytin osalta esitetään, että kyse ei ole Saussuren näkemyksistä vaan Harrisin tulkinnoista. Artikkelissa esitetään myös, että dynaamisuus ei ole yhteensopimaton käsite saussurelaisen kielikäsityksen kanssa.   On the critique of the Saussurean concept of language: some perspectives and counter-arguments The article deals with the critique of the Saussurean concept of language. The purpose of the article is to defend the Saussurean concept of language and to present Saussure as a more versatile thinker than may be assumed from a purely structuralist reading of Course. The article discusses the concept of language as a system (Saussure’s langue), the notion of context-free meaning, the so-called written-language bias, Roy Harris’ language myth, and the notion of dynamicity in language in relation to the Saussurean concept of language. The article begins by arguing that langue is both a methodological and an ontological concept that refers both to the unorganised rules of language and to the system of language rules as organised by the linguist. Second, the author asserts that some kind of permanence of meaning is essential to the concept of language as a communication system. Third, an argument is presented against the strong form of written-language bias, according to which, for instance, the analysis and reduction of continuous speech into discrete units is based on the model of written language. Fourth, the author posits that the language myth, developed by Harris, is not based on Saussure’s views but on Harris’ interpretation of Saussure’s views. The article ends with the contention that the notion of dynamicity is not incompatible with the Saussurean concept of language.

On the Probabilistic Nature of Observable Phenomena

2019 ◽  
Author(s):  
Muhammad Ali
Keyword(s):  
Quantum Mechanics ◽  
Complete Theory ◽  
Interpretation Of Quantum Mechanics ◽  
Multiple Realities ◽  
Lack Of Information ◽  
Complete Theories ◽  
Probabilistic Nature

This paper proposes a Gadenkan experiment named “Observer’s Dilemma”, to investigate the probabilistic nature of observable phenomena. It has been reasoned that probabilistic nature in, otherwise uniquely deterministic phenomena can be introduced due to lack of information of underlying governing laws. Through theoretical consequences of the experiment, concepts of ‘Absolute Complete’ and ‘Observably Complete” theories have been introduced. Furthermore, nature of reality being ‘absolute’ and ‘observable’ have been discussed along with the possibility of multiple realities being true for observer. In addition, certain aspects of quantum mechanics have been interpreted. It has been argued that quantum mechanics is an ‘observably complete’ theory and its nature is to give probabilistic predictions. Lastly, it has been argued that “Everettian - Many world” interpretation of quantum mechanics is very real and true in the framework of ‘observable nature of reality’, for humans.

Nonlinear dispersion hyperbolic models of continuous media

2007 ◽  
Vol 5 ◽  
pp. 273-278
Author(s):  
V.Yu Liapidevskii
Keyword(s):  
Boussinesq Equations ◽  
Nonlinear Dispersion ◽  
Order Of Accuracy ◽  
Flow Models ◽  
Wave Approximation ◽  
Long Wave ◽  
Primary Model ◽  
Nonequilibrium Flows ◽  
Internal Inertia ◽  
Long Wave Approximation

Nonequilibrium flows of an inhomogeneous liquid in channels and pipes are considered in the long-wave approximation. Nonlinear dispersion hyperbolic flow models are derived allowing taking into account the influence of internal inertia during the relative motion of phases upon the structure of nonlinear wave fronts. The asymptotic derivation of dispersion hyperbolic models is shown on the example of classical Boussinesq equations. It is shown that the hyperbolic approximation of the equations has the same order of accuracy as the primary model.

Moral Reasoning and the Primacy of the Practical

2018 ◽  
Author(s):  
Jonathan Dancy
Keyword(s):  
Moral Reasoning ◽  
Practical Reasoning ◽  
Complete Theory ◽  
Practical Reasons ◽  
Moral Thought

This chapter considers how to locate moral reasoning in terms of the structures that have emerged so far. It does not attempt to write a complete theory of moral thought. Its main purpose is rather to reassure us that moral reasoning—which might seem to be somehow both practical and theoretical at once—can be perfectly well handled using the tools developed in previous chapters. It also considers the question how we are to explain practical reasoning—and practical reasons more generally—by contrast with the explanation of theoretical reasons and reasoning offered in Chapter 4. This leads us to the first appearance of the Primacy of the Practical. The second appearance concerns reasons to intend.

A note on Lie nilpotent group rings

1992 ◽  
Vol 45 (3) ◽  
pp. 503-506 ◽  
Author(s):  
R.K. Sharma ◽  
Vikas Bist
Keyword(s):  
Nilpotent Group ◽  
Group Algebra ◽  
Group Rings ◽  
Group Of Units

Let KG be the group algebra of a group G over a field K of characteristic p > 0. It is proved that the following statements are equivalent: KG is Lie nilpotent of class ≤ p, KG is strongly Lie nilpotent of class ≤ p and G′ is a central subgroup of order p. Also, if G is nilpotent and G′ is of order pn then KG is strongly Lie nilpotent of class ≤ pn and both U(KG)/ζ(U(KG)) and U(KG)′ are of exponent pn. Here U(KG) is the group of units of KG. As an application it is shown that for all n ≤ p+ 1, γn(L(KG)) = 0 if and only if γn(KG) = 0.

Primitivity in representations of polycyclic groups

1980 ◽  
Vol 88 (1) ◽  
pp. 15-31 ◽  
Author(s):  
D. L. Harper
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Nilpotent Group ◽  
Infinite Dimension ◽  
Finitely Generated ◽  
Polycyclic Groups

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?

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