21.38 (2026)

(S. Harper, C. Donoven). The spread of a group $G$ is the greatest nonnegative integer $k$ such that for all nontrivial elements $x_1, \dots, x_k \in G$ there exists $y \in G$ such that $\langle x_1, y \rangle = \dots = \langle x_k, y \rangle = G$, or is $\infty$ in case there is no such maximum. Does there exist a group with spread equal to 1?