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Let $𝕂$ be a field, G a reductive algebraic $𝕂$-group, and G 1 ≤ G a reductive subgroup. For G 1 ≤ G, the corresponding groups of $𝕂$-points, we study the normalizer N = N G(G 1). In particular, for a standard embedding of the odd orthogonal group G 1 = SO(m, $𝕂$) in G = SL(m, $𝕂$) we have N ≅ G 1 ⋊ µm($𝕂$), the semidirect product of G 1 by the group of m-th roots of unity in $𝕂$. The normalizers of the even orthogonal and symplectic subgroup of SL(2n, $𝕂$) were computed in [Širola B., Normalizers and self-normalizing...