#### Vol. 12, No. 8, 2018

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
On the relative Galois module structure of rings of integers in tame extensions

### Adebisi Agboola and Leon R. McCulloh

Vol. 12 (2018), No. 8, 1823–1886
##### Abstract

Let $F$ be a number field with ring of integers ${O}_{F}$ and let $G$ be a finite group. We describe an approach to the study of the set of realisable classes in the locally free class group $Cl\left({O}_{F}G\right)$ of ${O}_{F}G$ that involves applying the work of McCulloh in the context of relative algebraic $K$ theory. For a large class of soluble groups $G$, including all groups of odd order, we show (subject to certain mild conditions) that the set of realisable classes is a subgroup of $Cl\left({O}_{F}G\right)$. This may be viewed as being a partial analogue in the setting of Galois module theory of a classical theorem of Shafarevich on the inverse Galois problem for soluble groups.

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/ant

We have not been able to recognize your IP address 44.192.94.86 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

or by using our contact form.