On Sylow Subgroups of Abelian Affine Difference Sets
An n-subsetD of a group G of order n2−1 is called an affine difference set of G relative to a normal subgroup N of G of order n−1 if the list of differences d1d2-1 (d1, d2 ∈ D, d1 ≠ d2) contain search element of G-N exactly once and no element of N. It is a well-known conjecture that if D is an affine difference set in an abelian group G, then for every prime p, the Sylow p-subgroup of G is cyclic. In Arasu and Pott , it was shown that the above conjecture is true when p = 2. In this paper we give some conditions under which the Sylow p-subgroup of G is cyclic.
Dizon-Garciano, A.V., Hiramine, Y. On Sylow Subgroups of Abelian Affine Difference Sets. Designs, Codes and Cryptography 22, 157–163 (2001). https://doi.org/10.1023/A:1008312921730