Since every linear automorphism of V fixes 0 our interest in the transitivity properties of GL(V) is confined to its action on V* = V - {0}. GL(V) is transitive on V* since any two elements of V* may be chosen as the initial members of two ordered bases; it is not in general 2-transitive because there is no linear automorphism taking an independent pair to a dependent pair.

In mathematics, automorphisms of algebraic structures play an important role. Automorphisms capture the symmetries inherent in the structures and many important results have been proved by analyzing the automorphism group of the structure.

A tame automorphism is a product of elementary automorphisms, and a non-tame automorphism is called wild. The “tame automorphism problem” asks whether any automorphism is tame.

Automorphism

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