On the Galois Cohomology of the Ring of Integers in an Algebraic Number Field

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1969Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 20, page 405 (issn: 0002-9939,

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Authors: Lee, M. P.; Madan, M. L.;

doi: 10.2307/2035664 , 10.1090/s0002-9939-1969-0236143-8

On the Galois Cohomology of the Ring of Integers in an Algebraic Number Field

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Abstract

On the basis of these results he conjectured in [9] that the groups Hr(G, OF) have the same order also in the case when G is not cyclic. In the present note, we shall show that the conjecture is false. We shall also demonstrate how the problem of determining Hr(G, OF) can be localized. In the end, we shall make some remarks concerning proofs of Theorems 1, 11 and III and give a generalization of Theorem I in the case where G is nilpotent.

Keywords

ring of integers, algebraic number field, Galois cohomology, Algebraic numbers; rings of algebraic integers

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