In this paper we consider the problem of classifying the isomorphism classes of extensions
of degree pk of a p-adic field K, restricting to the case of extensions without intermediate …

We present a family of algorithms for computing the Galois group of a polynomial defined
over ap-adic field. Apart from the “naive” algorithm, these are the first general algorithms for …

We present a collection of new algorithms and approaches to several aspects of p-adic
computation including:• computing the Galois group of a polynomial defined over a p-adic …

We give a brief re-exposition of the theory due to Pauli and Sinclair of ramification polygons
of Eisenstein polynomials over p-adic fields, their associated residual polynomials and an …

Given ap-adic field K and a prime number ℓ ℓ, we count the total number of the isomorphism
classes of p^ ℓ p ℓ-extensions of K having no intermediate fields. Moreover, for each group …

The subject of this thesis in the study of nite extensions of p-adic fields, in different aspects.
Via the study of the Galois module of p-th power classes L=(L) p of a general Galois …

Let p> 2 be prime, Qp be the field of p-adic numbers, and K be the unramified quadratic
extension of Qp. Amano (1971) has characterized the degree p extensions L of K, up to K …

We describe a method for counting the number of extensions of ℚ p with a given Galois
group G, founded upon the description of the absolute Galois group of ℚ p due to Jannsen …

Let Q_2 denote the field of 2-adic numbers, and let G be a group of order 2^ n for some
positive integer n. We provide an implementation in the software program GAP of an …

Let K be ap-adic field. Restricting to the case of no intermediate extensions, we obtain
formulæ counting the number of (totally and wildly) ramified extensions of degree p^ 4 p 4 of …