defined on the sets Ti(V) of i-dimensional subspaces of V. Obviously, these induced maps yield an automorphism of the projective plane PG(V). We define
Theorem. The group is the full automorphism group of the projective plane PG(V).
is an invariant subgroup of , called the projective group of PG(V). It equals the subgroup generated by all central-axial collineations of PG(V). Moreover,
is isomorphic to the group Out(K) of outer automorphisms of the skewfield K. In particular, we have if and only if each automorphism of K is an inner automorphism.