Related papers: The present state of the capitulation problem
This thesis deals with the capitulation problem in class field theory and gives various new insights into the subject.
In this paper, we establish two main results which give conditions necessary and sufficient for a $ 2 $-group metabelian such that $G/G'$ is of type $(2, 4)$ either metacyclic or not. If $G$ is the Galois group of…
Let \(\Gamma=\mathbb{Q}(\sqrt[3]{n})\) be a pure cubic field with normal closure \(k=\mathbb{Q}(\sqrt[3]{n},\zeta)\), where \(n>1\) denotes a cube free integer, and \(\zeta\) is a primitive cube root of unity. Suppose \(k\) possesses an…
We prove a capitulation result for locally free class groups of orders of group algebras over number fields. As a corollary, we obtain an "arithmetically disjoint capitulation result" for the Galois module structure of rings of integers.
This paper is a survey of author's mathematical and logical study of the problem of quantization of fields.
We study the capitulation of ideal classes in an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $k =Q(\sqrt{2pq}, i)$, where $i=\sqrt{-1}$ and $p\equiv -q\equiv1 \pmod 4$ are different primes. For each…
With the explosive growth of textual information, summarization systems have become increasingly important. This work aims to concisely indicate the current state of the art in abstractive text summarization. As part of this, we outline the…
We study the capitulation of $2$-ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $\mathbf{k} =\mathbb{Q}(\sqrt{p_1p_2q}, i)$, where $i=\sqrt{-1}$ and $p_1\equiv p_2\equiv-q\equiv1…
We establish a logarithmic version of the classical result of Artin-Furw{\"a}ngler on the principalization ofideal classes in the Hilbert class-field by applying the group theoretic description of the transfert map to logarithmic…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the…
The topic of the review is the application of new ideas of unconventional quantum states to the physics of condensed matter, in particular of solid state, in the context of modern field theory. A comparison is made with classical papers on…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
The investigation of the ideal class group $Cl_K$ of an algebraic number field $K$ is one of the key subjects of inquiry in algebraic number theory since it encodes a lot of arithmetic information about K. There is a considerable amount of…
We study a logarithmic version of the classical result of Artin-Furw{\"a}ngler on principalization of ideal classes in the Hilbert class-field by applying the group theoretic description of the transfert map to logarithmic class-groups of…
Subtraction games is a class of combinatorial games. It was solved since the Sprague-Grundy Theory was put forward. This paper described a new algorithm for subtraction games. The new algorithm can find win or lost positions in subtraction…
This is a brief description of what has been accomplished and what remains to be done in the construction of a nonperturbative formulation of "The Theory Formerly Known as String". It is culled from two short talks given by the author at…
As we go along with a bioinformatic analysis we stumbled over a new combinatorial question. Although the problem is a very special one, there are maybe more applications than only this one we have. This text is mainly about the general…
The mathematical aspects of the popular logic game Sudoku incorporate a significant number of the group theory concepts. In this note, we describe all symmetric transformations of the Sudoku grid. We do not intend to obtain a new strategy…
In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…