The character values of abelian difference sets often are contained in small subfields of the underlying cyclotomic field. One way to make use of this fact is to derive a bound on the absolute value of cyclotomic integers contained in these subfields. This approach leads to a general exponent bound for difference sets. In this talk, we present a different approach to utilize the reduction to subfields. We show that difference sets can be decomposed in a way that reflects the subfields the character values can be found in. This decomposition leads to strong necessary conditions on certain Sylow p-subgroups of abelian groups containing difference sets.

Back to Workshop Schedule