Obstructions de Brauer-Manin enti\`eres sur les espaces homog\`enes \`a stabilisateurs finis nilpotents

Let $k$ be a number field. We construct homogeneous spaces of $S{L}_{n,k}$ with finite nilpotent non-abelian stabilizers for which the Brauer-Manin obstruction does not explain the failure of strong approximation (resp. the failure of the integral Hasse principle).