Abstract

Let V be a nonsingular vector space over a field K of characteristic 2 with | K | > 3 . Suppose K is perfect and π is an element in the special orthogonal group SO ( V ) = Ω ( V ) with dim B ( π ) = 2 d . The length of π with respect to the symmetry commutators is d if B ( π ) is not totally isotropic; otherwise it is d + 1 .

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