Relative \((p^a, p^b, p^a, p^{a-b})\)-difference sets: A unified exponent bound and a local ring construction
After a short interesting historical updating the authors show that the exponent of an abelian group of order \(p^{2c+b}\) (\(p\) odd prime) containing a relative \((p^{2c},p^b,p^{2c},p^{2c-b})\)-difference set cannot exceed \(p^{c+1}\). Using local principal ideal rings (= chain rings) relative \((q^{2u},q,q^{2u},q^{2u-1})\)-difference sets (\(q\) a prime power) are construed. One of the difficult cases for the existence of \((p^a,p,p^a,p^{a-1})\)-difference sets is discussed in detail. As usual in this type of research, details are important and interesting but too complex to be quoted.
scientific article; zbMATH DE number 1421405
scientific article