Commutators of symmetries in characteristic 2

Ellers, Erich W. and Villa, Oliver (2011) Commutators of symmetries in characteristic 2. Linear Algebra and its Applications, 434 (6). pp. 1588-1593.

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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 dimB(π)=2d. 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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