13.63 (1995)

Let $\pi_e(G)$ denote the set of orders of elements of a group $G$. For $\Gamma \subseteq \mathbb{N}$ let $h(\Gamma)$ denote the number of non-isomorphic finite groups $G$ with $\pi_e(G) = \Gamma$. Is there a number $k$ such that, for every $\Gamma$, either $h(\Gamma) \leqslant k$, or $h(\Gamma) = \infty$?