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the group axioms (with neutral element ). The algebraic group is called the multiplicative group, because its -points are isomorphic to the multiplicative group of the field (an isomorphism is given by ; note that the subset of invertible elements does not define an algebraic subvariety in ).
* The special linear group is an algebraic group: it is given by the algebraic equation in the affine space (identified with the space of -by- matrices), multiplication of matrices is regular and the

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