Currently displaying 1 – 5 of 5

Showing per page

Order by Relevance | Title | Year of publication

A generalization of a result on integers in metacyclic extensions

James Carter — 1999

Colloquium Mathematicae

Let p be an odd prime and let c be an integer such that c>1 and c divides p-1. Let G be a metacyclic group of order pc and let k be a field such that pc is prime to the characteristic of k. Assume that k contains a primitive pcth root of unity. We first characterize the normal extensions L/k with Galois group isomorphic to G when p and c satisfy a certain condition. Then we apply our characterization to the case in which k is an algebraic number field with ring of integers ℴ, and, assuming some...

Some remarks on Hilbert-Speiser and Leopoldt fields of given type

James E. Carter — 2007

Colloquium Mathematicae

Let p be a rational prime, G a group of order p, and K a number field containing a primitive pth root of unity. We show that every tamely ramified Galois extension of K with Galois group isomorphic to G has a normal integral basis if and only if for every Galois extension L/K with Galois group isomorphic to G, the ring of integers O L in L is free as a module over the associated order L / K . We also give examples, some of which show that this result can still hold without the assumption that K contains...

Page 1

Download Results (CSV)