Graham's rearrangement for dihedral groups

Abstract: A famous conjecture of Graham asserts that every set $A \subseteq \mathbb{F}p \setminus {0}$ can be ordered so that all partial sums are distinct. Bedert and Kravitz proved that this statement holds whenever $|A| \leq e^{c(\log p)^{1/4}}$. In this paper, we will use a similar procedure to obtain an upper bound of the same type in the case of dihedral groups $Dih{p}$.