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Proceedings - Mathematical Sciences, 2017 We give, in Sections 2 and 3, an english translation of: {\it Classes généralisées invariantes}, J. Math. Soc. Japan, 46, 3 (1994), with some improvements and with notations and definitions in accordance with our book: {\it Class Field Theory: from theory to practice}, SMM, Springer-Verlag, $2^{\rm nd}$ corrected printing 2005. We recall, in Section 4,
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