The 3-zero-sum partition property conjecture

Let $\Gamma$ be a finite Abelian group, and let $I(\Gamma)$ denote its set of involutions. The 3-zero-sum partition property conjecture. If $|I(\Gamma)|>1$, then $\Gamma$ has the 3-Zero-Sum Partition Property: for every partition $\{m_i\}_{i=1}^t$ of $|\Gamma|-1$ with $m_i\geq 3$ for all $i$, the nonzero elements of $\Gamma$ can be partitioned into subsets of these respective sizes, each having sum zero. The conjecture is proved in the paper for groups of order $2^n$; the other even-order cases with more than one involution remain open.