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|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||09 Oct 2012 11:49|