Automorphism Group Schemes of Basic Matrix Invariants

Invariants of finite group schemes

Let k be an algebraically closed field, G a finite group scheme over k operating on a scheme X over k. Under assumption that X can be covered by G-invariant affine open subsets the classical results in [3] and [14] describe the quotient X/G. In case of a free action X is known to be a principal homogeneous G-space over X/G. Furthermore, the category of G-linearized quasi-coherent sheaves of OX ...

Basic Theory of Affine Group Schemes

AUTOMORPHISM GROUP OF GROUPS OF ORDER pqr

H"{o}lder in 1893 characterized all groups of order $pqr$ where  $p>q>r$ are prime numbers. In this paper,  by using new presentations of these groups, we compute their full automorphism group.

THE AUTOMORPHISM GROUP OF FINITE GRAPHS

Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.

The Automorphism Group of a Lie Group

Introduction. The group A (G) of all continuous and open automorphisms of a locally compact topological group G may be regarded as a topological group, the topology being defined in the usual fashion from the compact and the open subsets of G (see §1). In general, this topological structure of A(G) is somewhat pathological. For instance, if G is the discretely topologized additive group of an i...