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2013•Annales Universitatis Mariae Curie-Sklodowska sectio A – MathematicaOpen access

Some results on local fields

Akram Lbekkouri

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Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Abelian group, Mathematics, Abelian extension, Extension (predicate logic), Local field, Exponent, Pure mathematics, Galois group

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