Related papers: Tannakian Fundamental Groups Associated to Galois …
We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.
We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set V^G of G-invariants.
This is an almost self-contained monograph (containing some new results) on left-orderable groups which mostly rely on dynamical and probabilistic aspects, but also on geometric, combinatorial, analytic, and topological ones. This new…
Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to…
In this article, we study the various fundamental groupoid schemes corresponding to Tannakian categories of certain types of vector bundles. We compute fundamental groupoid scheme of anisotropic conic, Klein bottle and abelian varieties.…
Let K be a number field and let f(x) = x^q + c where q is a prime power, c is in K, and f is not post-critically finite. We show that for any strictly preperiodic b in K, the iterated Galois group at b with respect to f has finite index in…
This paper is a sequel of the reference \cite[\S 4.2, p.p. 1782--1783]{almp}, in where some families of quadratic polynomial vector fields related with orthogonal polynomials were studied. We extend such results that contain some details…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
It is well known that the Galois group of an extension puts constraints on the structure of the relative ideal class groups. Using only basic parts of the theory of group representations, we give a unified approach to such results.
We revisit Kolchin's results on definability of differential Galois groups of strongly normal extensions, in the case where the field of constants is not necessarily algebraically closed. In certain classes of differential topological…
We study the action of the absolute Galois group on the fundamental groups.
Our aim of this and subsequent papers is to enlighten (a part of, presumably) arithmetic structures of knots. This paper introduces a notion of profinite knots which extends topological knots and shows its various basic properties.…
We show that finitely presented groups which admit $k$-planar Cayley graphs contain finite-index subgroups with planar Cayley graphs. More generally, we answer a question of Georgakopoulos and Papasoglu in the special case of coarsely…
In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…
We prove some new results related to Tanaka's formula.
Several questions about the Galois group of field generated by certain one dimensional formal group laws are studied. This is continuation of author's prior article titled 'Field Generated by Division Points of Certain Formal Group Laws -…
We study the behaviour of the topological fundamental group under totally ramified abelian covers (a special case of abelian Galois covers) of complex projective varieties of dimension at least 2.
This paper deals with criteria of algebraic independence for the derivatives of solutions of rank one difference equations. The key idea consists in deriving from the commutativity of the differentiation and difference operators a sequence…
We extend the theory of countably generated Demushkin groups to Demushkin groups of arbitrary rank. We investigate their algebraic properties and invariants, count their isomorphism classes and study their realization as absolute Galois…
This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…