Local automorphisms of some classical groups

TL;DR

This paper studies local automorphisms of classical groups, showing that in some cases they are automorphisms and in others closely related to automorphisms.

Contribution

It characterizes when local automorphisms of certain classical groups are actual automorphisms or closely related to them.

Findings

In some classical groups, local automorphisms are automorphisms.

In other cases, local automorphisms are closely related to automorphisms.

Provides a classification of local automorphisms for these groups.

Abstract

A map on a group into itself is called a local automorphism if at any two points of the group, it can be interpolated by an automorphism of that group. In this paper we investigate the question of how local automorphisms of some classical groups are related to automorphisms. In some cases it turns out that the local automorphisms are in fact automorphisms. In the remaining cases we show that the local automorphisms are still closely related to the automorphisms.