ABSTRACT
M y vague search for active collaborative research had resounding success in the spring of 1941 when, at the end of my first three-year appointment as an assistant professor at Harvard, I enjoyed a one-semester research leave. I spent some of the time in Chicago collaborating with Otto Schilling, who had been appointed to the department there after my departure. Schilling and I had just completed a long paper on non-abelian class field theory; we were also working on a new and generalized Kummer theory. The class field theory made heavy use of crossed product algebras and their factor sets; some of our calculations suggested that we were missing something beyond factor sets, but we did not know what it might be. Fascinated by these factor sets, I also began to study their uses in the construction of group extensions.
