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10aGalois module structure for ArtinSchreier theory over bicyclic extensions 
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1 aHeller, Laurenecreatorulheller@wellesley.edu 
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1 aSchultz, Andreweadvisor 
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2 aMathematicsedepartment 
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7aAcademic theses2lcgft 
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k2017 
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g2017 
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aIf K/F is a Galois field extension with Galois group of prime power order distinct from char(F), then Gal(K/F) acts on pth power classes of K. The structure of the resulting module is known for Gal(K/F) isomorphic to a cyclic group of prime power order or the Klein 4group. We use ArtinSchreier theory to produce a similar decomposition for characteristic p extensions with bicyclic Galois groups of exponent p. 