Alspach–Liversidge rearrangement conjecture

Establish that every subset of the nonzero elements of every finite abelian group is rearrangeable, meaning that its elements can be ordered with pairwise distinct partial products.

Background

The conjecture generalizes Graham’s rearrangement problem from prime cyclic groups to arbitrary finite abelian groups. The paper proves only asymptotic or restricted-case results and states the exact assertion as a conjecture.

References

For any finite abelian group $\Gamma$, any subset $S\subseteq \Gamma\setminus{0}$ is rearrangeable.

— Towards Graham's rearrangement conjecture via rainbow paths  (2503.01825 - Bucić et al., 3 Mar 2025) in Conjecture 2, Section 1