Related papers: Fixed Sets of Automorphisms of Countable, Arithmet…

We consider a self-homeomorphism h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F. With Le Calvez' transverse foliations theory in…

An automorphism of a spherical building is called \textit{domestic} if it maps no chamber onto an opposite chamber. This paper forms a significant part of a large project classifying domestic automorphisms of spherical buildings of…

Let $G$ be a linear algebraic group, over a field $F$. We show that $G$ is isomorphic to the automorphism group scheme of a smooth projective $F$-variety, defined as the blow-up of a projective space, along a suitable smooth subvariety.

Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a…

Consider a smooth connected algebraic group $G$ acting on a normal projective variety $X$ with an open dense orbit. We show that Aut($X$) is a linear algebraic group if so is $G$; for an arbitrary $G$, the group of components of Aut($X$) is…

In a recent paper [3], the authors introduced a map $\mathcal{F}$ which associates a Deitmar scheme (which is defined over the field with one element, denoted by $\mathbb{F}_1$) with any given graph $\Gamma$. By base extension, a scheme…

Let $\sigma$ be an automorphism of a field $K$ with fixed field $F$. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras $K[t;\sigma]/fK[t;\sigma]$ obtained…

In this paper, we investigate the existence of fixed-point-free automorphisms for finite-dimensional Lie algebras. By a result of Jacobson, a Lie algebra admitting a fixed-point-free automorphism is solvable. We prove that such a Lie…

We consider automorphism groups of some countably categorical structures and their precompact expansions. We prove that automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows. We also study…

We present three examples of countable homogeneous structures (also called Fraisse limits) whose automorphism groups are not universal, namely, fail to contain isomorphic copies of all automorphism groups of their substructures. Our first…

We give elementary proofs of the following two theorems on automorphisms of a finite group G: (1) An automorphism of G is inner if and only if it extends to an automorphism of every finite group containing G. (2) There exists a finite…

We define a graph structure associated in a natural way to finite fields that nevertheless distinguishes between different models of isomorphic fields.

We call a flag variety admissible if its automorphism group is the projective general linear group. (This holds in most cases.) Let $K$ be a field of characteristic $0$, containing all roots of unity. Let the $K$-variety $X$ be a form of an…

Let $S$ be a semigroup, let $n\in\mathbb{N}$ be a positive natural number, let $A,B\subseteq S$, let $\mathcal{U},\mathcal{V}\in\beta S$ and let let $\mathcal{F}\subseteq\{f:S^{n}\rightarrow S\}$. We say that $A$ is $\mathcal{F}$-finitely…

We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…

Let $\mathcal{L}$ be a centric linking system associated to a saturated fusion system on a finite $p$-group $S$. An automorphism of $\mathcal{L}$ is said to be rigid if it restricts to the identity on the fusion system. An inner rigid…

Motivated by classic theorems of Thompson and Berger on the Fitting height of finite groups with a fixed-point-free automorphism of coprime order, we conjecture that, for every non-zero polynomial $f(x) = a_0 + a_1 x + \cdots + a_d x^d \in…

Let G be a countable group. We proof that there is a model companion for the approximate theory of a Hilbert space with a group G of automorphisms. We show that G is amenable if and only if the structure induced by countable copies of the…

Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…

It is shown that if a finite generically smooth morphism $f\,:\,Y\,\longrightarrow\, X$ of smooth projective varieties induces an isomorphism of the \'etale fundamental groups, then the induced map of the stratified fundamental groups…