Radial automorphism

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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.