The Automorphism Group of a Homogeneous Almost Complex Manifold

The Automorphism Group of a Homogeneous Almost Complex Manifold (*)

A Bound for the Dimension of the Automorphism Group of a Homogeneous Compact Complex Manifold

Let X be a homogeneous compact complex manifold, and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. Examples show that dim Aut(X) can grow exponentially in n = dimX. In this note it is shown that dim Aut(X) ≤ n − 1 + (2n− 1 n− 1 ) when n ≥ 3. Thus, dim Aut(X) is at most exponential in n. The proof relies on an upper bound for the dimension of the space of sections of the...

The Automorphism Group of a Finite p-Group is Almost Always a p-Group

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism group of a finite p-group is almost always a p-group. The asymptotics in our theorem involve fixing any two of the following parameters and letting the thir...

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold

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.