Quinn's Hyperelementary Induction Conjecture

Let $G$ be a group, and let $\overline{{\mathcal H}}$ be the class of possibly infinite hyperelementary groups. Say that a group satisfies induction for a class of groups when the relevant induction statement holds for that class. Hyperelementary Induction Conjecture. All groups satisfy induction for the class $\overline{{\mathcal H}}$ of possibly infinite hyperelementary groups. The conjecture concerns extending hyperelementary induction from finite groups to possibly infinite hyperelementary groups; the source attributes it to Quinn and does not state a resolution.