3 problems

Let $\mathbb{Z}_m$ be a cyclic group of order $m=2^n$. Let $t$ and $m_1,\ldots,m_t$ be positive integers satisfying … with $m_1\geq 1$ and $m_i\geq 2$ for $2\leq i\leq t$. Equal-su…

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…

Let $\Gamma$ be an Abelian group in $\mathcal{G}$, where $\mathcal{G}$ denotes the class used in the paper, and let $g_0$ be its identity element. Suppose that $\Gamma$ has even or…