21.106 (2026)
OpenA first order formula $\phi(x)$ in the group language with one free variable is said to be concise in a class $\mathcal{C}$ of groups if for every group $G$ in $\mathcal{C}$ such that the set $G_\phi$ of elements in $G$ satisfying $\phi$ is finite, the subgroup $\phi(G)$ generated by $G_\phi$ is also finite (cf. 21.105 and 2.45). Is every formula with one free variable concise in the class of residually finite groups?
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