19.68 (2018)

For a finite group $G$ and a permutation group $K$, let $b_G(K)$ denote the number of conjugacy classes of regular subgroups of $K$ isomorphic to $G$. Does there exist a function $f$ such that $b_G(K) \leqslant n^{f(r)}$ for every abelian group $G$ of order $n$ and rank $r$, and every group $K$ such that $K^{(2)} = K$? (See 19.67 for the definition of $K^{(2)}$.)