Let V be an n-dimensional regular quadratic space over a field K of characteristic not 2. Assume n ≥ 4. Let W be a regular hyperplane and v a nonzero vector orthogonal to W. Suppose every regular hyperplane in W is universal. If σ is an isometry of V not leaving W invariant, then σ, together with the isometries of W, generate the orthogonal group of V, with one exception.
KeywordsMaximal Subgroup Orthogonal Group Nonzero Vector Quadratic Space Regular Quadratic Space
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