Genus number and l-rank of genus group of cyclic extensions of degree l

1982 ◽  
Vol 39 (1) ◽  
pp. 99-109
Author(s):  
Teruo Takeuchi
Keyword(s):  
Genus Number

On the class number of the lpth cyclotomic number field

1991 ◽  
Vol 109 (2) ◽  
pp. 263-276
Author(s):  
Norikata Nakagoshi
Keyword(s):  
Number Field ◽  
Class Number ◽  
Prime Factor ◽  
Analytic Formula ◽  
Cyclotomic Number ◽  
Class Number Formula ◽  
Prime Factors ◽  
Number Formula ◽  
Genus Number ◽  
Analytic Class

The first factor of the class number of a cyclotomic number field can be obtainable by the analytic class number formula and there are some tables which show the decompositions of the first factors into primes. But, using just the analytic formula, we cannot tell what kinds of primes will appear as the factors of the class number of a given cyclotomic number field, except for those of the genus number, or the irregular primes. It is significant to find in advance the prime factors, particularly those prime to the degree of the field. For instance, in the table of the first factors we can pick out some pairs (l, p) of two odd primes l and p such that the class number of each lpth cyclotomic number field is divisible by l even if p 1 (mod l). If p ≡ (mod l) for l ≥ 5 or p ≡ 1 (mod 32) for l = 3, then it is easy from the outset to achieve our intention of finding the factor l using the genus number formula. Otherwise it seems to be difficult. We wish to make it clear algebraically why the class number has the prime factor l.

scholarly journals CONDENSED MATTER PHYSICS OF BIOMOLECULE SYSTEMS IN A DIFFERENTIAL GEOMETRIC FRAMEWORK

2007 ◽  
Vol 21 (13n14) ◽  
pp. 2475-2492
Author(s):  
HENRIK BOHR ◽  
JOHN H. IPSEN ◽  
STEEN MARKVORSEN
Keyword(s):  
Catalytic Properties ◽  
Condensed Matter ◽  
Vesicle Formation ◽  
Condensed Matter Physics ◽  
Biomolecular Systems ◽  
Geometric Framework ◽  
Geometric Methods ◽  
And Topology ◽  
Structure Of Proteins ◽  
Genus Number

In this contribution biomolecular systems are analyzed in a framework of differential geometry in order to derive important condensed matter physics information. In the first section lipid bi-layer membranes are examined with respect to statistical properties and topology, e.g. a relation between vesicle formation and the proliferation of genus number. In the second section differential geometric methods are used for analyzing the surface structure of proteins and thereby understanding catalytic properties of larger proteins.

scholarly journals TOPOLOGICAL INVARIANTS AND ANYONIC PROPAGATORS

1999 ◽  
Vol 14 (28) ◽  
pp. 1933-1936 ◽  
Author(s):  
WELLINGTON DA CRUZ
Keyword(s):  
Hausdorff Dimension ◽  
Integral Representation ◽  
Particle Flux ◽  
Topological Invariant ◽  
Topological Invariants ◽  
Continuous Family ◽  
Path Integral Representation ◽  
Flux System ◽  
Fractal Properties ◽  
Genus Number

We obtain the Hausdorff dimension, h=2-2s, for particles with fractional spins in the interval, 0≤ s ≤0.5, such that the manifold is characterized by a topological invariant given by, [Formula: see text]. This object is related to fractal properties of the path swept out by fractional spin particles, the spin of these particles, and the genus (number of anyons) of the manifold. We prove that the anyonic propagator can be put into a path integral representation which gives us a continuous family of Lagrangians in a convenient gauge. The formulas for, h and [Formula: see text], were obtained taking into account the anyon model as a particle-flux system and by a qualitative inference of the topology.

scholarly journals The Ancient Greek adjective: semantic and grammatical features

2020 ◽  
Keyword(s):  
Semantic Analysis ◽  
Word Formation ◽  
Morphological Features ◽  
Ancient Greek ◽  
Historical Process ◽  
Lexical Meaning ◽  
Part Of Speech ◽  
Syntactic Features ◽  
General Meaning ◽  
Genus Number

The article reveals the essence of an Ancient Greek adjective as a separate part of speech. Thus, the substantive nature of an adjective was examined, including the historical process of its separation as an independent part of speech, with a consequent emphasis on the inseparability of adjectives and nouns by external signs in Ancient Greek. The analysis of the Greek adjectives was made on the grounds of their semantics, morphological features, syntactic functions. The semantic analysis was based on the studying of such concepts as the categorial, word-building and lexical meaning. The categorial meaning is the attribution of an adjective. The smaller semantic-grammatical groups (qualitative, relative and possessive adjectives) were learnt with regard to word formation and lexical motivation. Word-building and lexical meanings were studied basing on the division of adjectives into primary units and derivatives. The meaning of a derivative is interpreted both: due to the analysis of its structure (paying a special attention to the compound units, which are mainly formed on the basis of word combinations), and due as to the relation (strong, weak, metaphorical) of the general meaning of a derivative with the meaning of its components. The word-formation meaning of such units, therefore, is syntagmatic. Their lexical semantics depend also on the context. The basic morphological categories of genus, number and case of a Greek adjective simultaneously indicates its semantic dependence on a noun. The category of degrees of comparison was analyzed on terms of morphological means and such syntactic features as left/right-side valence. The main primary (an attribute) and the secondary (as a predicative) syntactic adjective functions are equally realized in preposition or postposition to the noun in Ancient Greek.

scholarly journals The Genus Field and Genus Number in Algebraic Number Fields

1967 ◽  
Vol 29 ◽  
pp. 281-285 ◽  
Author(s):  
Yoshiomi Furuta
Keyword(s):  
Number Field ◽  
Algebraic Number ◽  
Algebraic Number Field ◽  
Number Fields ◽  
Abelian Extension ◽  
Normal Extension ◽  
Finite Degree ◽  
Algebraic Number Fields ◽  
Genus Field ◽  
Genus Number

Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.

Sign in / Sign up

Export Citation Format

Share Document