# Projective group

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in variables over a skew-field The group of transformations of the -dimensional projective space induced by the linear transformations of . There is a natural epimorphism with as kernel the group of homotheties (cf. Homothety) of , which is isomorphic to the multiplicative group of the centre of . The elements of , called projective transformations, are the collineations (cf. Collineation) of . Along with , which is also called the full projective group, one also considers the unimodular projective group , and, in general, groups of the form , where is a linear group.

For the group is simple, except for the two cases and or 3. If is the finite field of elements, then  How to Cite This Entry:
Projective group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Projective_group&oldid=18829
This article was adapted from an original article by E.B. Vinberg (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article