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Normalizers and self-normalizing subgroups II

Boris Širola (2011)

Open Mathematics

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...

Normes p -adiques et extensions quadratiques

Christophe Cornut (2009)

Annales de l’institut Fourier

On classifie les orbites de H sur l’immeuble de Bruhat-Tits de G pour trois paires sphériques ( G , H ) de groupes p -adiques classiques.

Obstruction sets and extensions of groups

Francesca Balestrieri (2016)

Acta Arithmetica

Let X be a nice variety over a number field k. We characterise in pure “descent-type” terms some inequivalent obstruction sets refining the inclusion X ( k ) é t , B r X ( k ) B r . In the first part, we apply ideas from the proof of X ( k ) é t , B r = X ( k ) k by Skorobogatov and Demarche to new cases, by proving a comparison theorem for obstruction sets. In the second part, we show that if k are such that E x t ( , k ) , then X ( k ) = X ( k ) . This allows us to conclude, among other things, that X ( k ) é t , B r = X ( k ) k and X ( k ) S o l , B r = X ( k ) S o l k .

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