Radial automorphism

Definition
Suppose $$G$$ is a group. A radial automorphism of $$G$$ is an automorphism of the form:

$$g \mapsto g \chi(g)$$

where $$\chi$$ is a homomorphism from $$G$$ to the center of $$G$$.

The group of all radial automorphisms is termed the radial automorphism group.

Radial automorphisms play an important role in the endomorphism structure of general linear groups.