Related papers: Computing the Automorphism Groups of Hyperelliptic…

We classify the pairs $(X,\pi)$, where $\pi\colon X\to S$ is a $\mathbb{P}^1$-bundle over a non-rational geometrically ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

In this paper we define a pair of faithful functors that map isomorphic and isotopic finite-dimensional algebras over finite fields to isomorphic graphs. These functors reduce the cost of computation that is usually required to determine…

Almost automorphy in the context of hyperfunctions is the main aim of this work. We give different equivalent definitions of almost automorphic hyperfunctions and then we study this class of hyperfunctions.

We compute an explicit representation of the (topological) automorphism group or a particular Toeplitz subshift. The automorphism group is a (non-finitely generated) subgroup of rational numbers under addition and the shift map corresponds…

We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by…

The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.

This paper addresses the question: given a scalar group, can we determine all the additions that transform this scalar group into a (near-)field? A key approach to addressing this problem involves transporting (near-)field structures via…

The formal group law of an elliptic curve has seen recent applications to computational algebraic geometry in the work of Couveignes to compute the order of an elliptic curve over finite fields of small characteristic. The purpose of this…

We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

We give a formula for computing the characteristic polynomial for certain hyperplane arrangements in terms of the number of bipartite graphs of given rank and cardinality.

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

In this note, we determine which automorphism subgroups of $\mathrm{Aut}_{\mathbb{F}_q}(\mathbb{F}_q((x)))$ are corresponding to $\mathbb{Z}_p$-extensions or $\mathbb{Z}_p\times\mathbb{Z}_p$-extensions of characteristic $0$ fields.

For a field $\mathbb{K}$ of characteristic $p\ge5$ containing $\mathbb{F}_{p}^{\operatorname{alg}}$ and the elliptic curve $E_{s,t}: y^{2} = x^{3} + sx + t$ defined over the function field $\mathbb{K}\left(s,t\right)$ of two variables $s$…

We develop techniques for computing the AK invariant of a domain with arbitrary characteristic. We use these techniques to describe for any field $K$ the automorphism group of $K[X,Y,Z]/(X^n Y - Z^2 - h(X)Z)$, where $h(0) \ne 0$ and $n \geq…

We compute explicitly the automorphism and outer automorphism group of all large-type free-of-infinity Artin groups. Our strategy involves reconstructing the associated Deligne complexes in a purely algebraic manner, i.e. in a way that is…

In this article, we will show that the automorphism group of any hypergraph is essentially equal to the determinant of some matrix over a ring generated from the set of ground points. With this, we are also able to determine whether two…

We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.

Let $\epsilon>0$. In this article we will present a deterministic algorithm which does the following. The input is a hyperelliptic curve $C$ of genus $g$ over a finite field $k$ of cardinality $q$ given by $y^2+h(x)y=f(x)$ such that the…