Journal of Prime Research in Mathematics

# On the arithmetical structure of some compact subsets in the $$p-$$adic complex number field

Angel Popescu
Department of Mathematics, Technical University of Civil Engineering of Bucharest, Romania.

$$^{1}$$Corresponding Author: popescuangel@yahoo.co.uk

### Abstract

We use arithmetical tools (algebraic numbers, valuations, Galois groups) in order to describe the structure of all compact subsets of the $$p-$$adic complex field, which are invariant with respect to the absolute Galois group of the $$p-$$adic number field

#### Keywords:

Galois groups, number fields, Banach algebras, compact sets.