21.97 (2026)
Open(M. Tărnăuceanu). Is it true that for every positive rational number $r$ there exists a finite group $G$ such that $|\text{Aut}(G)|/|G| = r$?
A similar question is answered in the positive for graphs, monoids, partial groups, and posets (R. Molinier, Preprint, 2025, https://arxiv.org/abs/2504.21059).
It is also known that the set $\{|\text{Aut}(G)|/|G|: G$ is a finite abelian group$\}$ is dense in $[0, +\infty)$ (M. Tărnăuceanu, Elemente Math. (2025), https://ems.press/journals/em/articles/14298544).
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