Abstract:
This report is an expository article that gathers and proves some of the results of a certain
unpublished paper (F. Chemotti, J. Min´aˇc, and J. Swallow. Galois module structure of square classes of units of Klein 4-group
extensions. April 2006. Unpublished preprint.) co-authored by Prof. John Swallow of Davidson College. For this paper,
I assume familiarity with abstract algebra at the level of MATH 251 and point-set topology at
the level of MATH 205. I also assume the reader has had some experience with infinite Galois
theory; cohomology of profinite groups; operations on the cohomology of profinite groups, including
conjugation, inflation, corestriction, and cup-product; Kummer theory; and Brauer groups. However,
all of these latter topics will be quickly reviewed within this report in Chapter 3.
