minac@uwo.ca, arwadsworth@ucsd.edu

Submission: 2003, Apr 10

We investigate the first two Galois cohomology groups of p-extensions over a base field which does not necessarily contain a primitive pth root of unity. We use twisted coefficients in a systematic way. We describe field extensions which are classified by certain residue classes modulo p^nth powers of a related field, and we obtain transparent proofs and slight generalizations of some classical results of Albert. The potential application to the cyclicity question for division algebras of degree p is outlined.

2000 Mathematics Subject Classification:

Keywords and Phrases:

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