Displaying similar documents to “Superprimes and a generalized Frobenius symbol”

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

Chipchakov, I. (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20. This paper gives a characterization of Henselian discrete valued fields whose finite abelian extensions are uniquely determined by their norm groups and related essentially in the same way as in the classical local class field theory. It determines the structure of the Brauer groups and character groups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms...

Some results on local fields

Akram Lbekkouri (2013)

Annales UMCS, Mathematica

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Let K be a local field with finite residue field of characteristic p. This paper is devoted to the study of the maximal abelian extension of K of exponent p−1 and its maximal p-abelian extension, especially the description of their Galois groups in solvable case. Then some properties of local fields in general case are studied too.

The class number one problem for some non-abelian normal CM-fields of degree 24

F. Lemmermeyer, S. Louboutin, R. Okazaki (1999)

Journal de théorie des nombres de Bordeaux

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We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to 𝒜 4 , the alternating group of degree 4 and order 12 . There are two such fields with Galois group 𝒜 4 × 𝒞 2 (see Theorem 14) and at most one with Galois group SL 2 ( 𝔽 3 ) (see Theorem 18); if the generalized Riemann hypothesis is true, then this last field has class number 1 .