On Lander’s conjecture for difference sets whose order is a power of 2 or 3.

Let p be a prime and let b be a positive integer. If a ( v, k, λ, n) difference set D of order n = p ^b exists in an abelian group with cyclic Sylow p-subgroup S, then $${p\in\{2,3\}}$$ and | S| = p. Furthermore, either p = 2 and v ≡ λ ≡ 2 (mod 4) or the parameters of D belong to one of four families explicitly determined in our main theorem. [ABSTRACT FROM AUTHOR]