The generalized Erdős–Ginzburg–Ziv conjecture for finite groups

Let $G$ be a finite group. For a sequence over $G$, let ${\mathsf d}(G)$ denote the maximal length of a zero-sum free sequence, and let ${\mathsf E}_m(G)$ denote the least integer $n$ such that every sequence over $G$ of length at least $n$ contains $m$ disjoint subsequences, each of length $|G|$ and each having sum zero in $G$.

Generalized Erdős–Ginzburg–Ziv conjecture. For every finite group $G$,

$${\mathsf E}_m(G)={\mathsf d}(G)+m|G|.$$

The equality is known for finite Abelian groups, nilpotent groups, groups of the form $C_m\ltimes_\varphi C_{mn}$, dihedral and dicyclic groups, and all non-Abelian groups of order $pq$ with $p$ and $q$ prime. The conjecture proposes that it holds for every finite group.