Related papers: Inner automorphisms of groupoids

Let $G$ be a group. An automorphism of $G$ is called intense if it sends each subgroup of $G$ to a conjugate; the collection of such automorphisms is denoted by $\mathrm{Int}(G)$. In the special case in which $p$ is a prime number and $G$…

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…

An automorphism of a graph $G=(V,E)$ is a bijective map $\phi$ from $V$ to itself such that $\phi(v_i)\phi(v_j)\in E$ $\Leftrightarrow$ $v_i v_j\in E$ for any two vertices $v_i$ and $v_j$. Denote by $\mathfrak{G}$ the group consisting of…

The paper follows two interconnected directions. 1. Let $G$ be a Roelcke precompact closed subgroup of the group $\Sym(\omega)$ of permutations of the natural numbers. Then $\Inn(G)$ is closed in $\Aut(G)$, where $\Aut(G)$ carries the…

The aim of this paper is to provide a definition of groupoid and cogroupoid internal to a category which makes use of only one object and morphisms, in contrast with the two object approach commonly found in the literature. We will give…

The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…

Let $G$ be a finite $p$-group such that $x\Z(G) \subseteq x^G$ for all $x \in G- \Z(G)$, where $x^G$ denotes the conjugacy class of $x$ in $G$. Then $|G|$ divides $|\Aut(G)|$, where $\Aut(G)$ is the group of all automorphisms of $G$.

It is shown that in various categories, including many consisting of maps or hypermaps, oriented or unoriented, of a given hyperbolic type, every countable group $A$ is isomorphic to the automorphism group of uncountably many non-isomorphic…

Let $H$ be an additively written monoid and let $\mathcal{P}_{0}(H)$ denote the reduced power monoid of $H$, that is, the monoid consisting of all subsets of $H$ containing $0$ with set addition as operation. Following work of Tringali, Wen…

We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.

We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…

For a real semisimple Lie algebra, we consider its automorphism group quotient by its identity component. This is known as the outer automorphism group. In this article, we compute the outer automorphism groups of all real semisimple Lie…

Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group…

The structure groups of non-degenerate symmetric set-theoretical solutions of the quantum Yang-Baxter equation provide an infinite family of Garside groups with many interesting properties. Given a non-degenerate symmetric solution, we…

We prove two conjectures on the automorphism group of a one-dimensional formal group law defined over a field of positive characteristic. The first is that if a series commutes with a nontorsion automorphism of the formal group law, then…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

Let $G$ be a reductive group over a number field $F$, which is split at a finite place $\mathfrak{p}$ of $F$, and let $\pi$ be a cuspidal automorphic representation of $G$, which is cohomological with respect to the trivial coefficient…

We show that several classes of groups G of PL-homeomorphisms of the real line admit non-trivial homomorphisms from G to the additive group of reals that are fixed by every automorphism of G. The classes of groups enjoying the stated…

A partial automorphism of a finite graph is an isomorphism between its vertex induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoid under composition (of partial maps). We describe the…