We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham e-Theses
You are in:

On the Galois module structure of units in met acyclic extensions

McGaul, Karen Yvonne (1996) On the Galois module structure of units in met acyclic extensions. Doctoral thesis, Durham University.



Let Г be a metacyclic group of order pq with p and q prime. We shall show that the Г-cohomology and character of a Г-lattice determine its genus. Let N/L be a Galois extension with group Г, then U(_N), the torsion-free units of N, is a Г-lattice and the isomorphism Q o U(_N) = Q o ɅS(_oo) gives its character. In certain cases we can determine its cohomology and thus its genus; in particular, when = h(_N) = 1 and L = Q we show that the genus of U(_N) depends only on the number of non-split, ramified primes in N/L. We shall also investigate U(_N) in the factorizability defect Grothendieck group.

Item Type:Thesis (Doctoral)
Award:Doctor of Philosophy
Thesis Date:1996
Copyright:Copyright of this thesis is held by the author
Deposited On:09 Oct 2012 11:49

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitter