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Title: On the Galois module structure of units in met acyclic extensions
Author: McGaul, Karen Yvonne
ISNI:       0000 0001 3624 1533
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 1996
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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.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Pure mathematics Mathematics