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Nous déterminons tous les corps diédraux à multiplication complexe de nombres de classes relatif un, puis ceux de nombre de classes un : il y a 32 tels corps non-abéliens principaux. C’est le premier exemple, dans ce cadre assez général, de résolution du problème de nombre de classes un pour les corps galoisiens à multiplication complexe avec un type de groupe de Galois non-abélien fixé.
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