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Fundamental theorem of projective geometry
Fundamental theorem of affine geometry
Let V be a non-zero vector space over a skewfield K. A bijective map f of V onto itself is called semilinear if there exists an automorphism of the skewfield K such that

for all elements x,y of V and a of K.

The set of all semilinear maps is a group, and the map which assigns to each semilinear map f the corresponding automorphism of K is a homomorphism with kernel GL(V). In particular, the linear group GL(V) is an invariant subgroup of with

Contributed by Hauke Klein
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