Structure of $k$-closures of finite nilpotent permutation groups

Dmitry Churikov

Let $G$ be a permutation group on a set $\Omega$, and $k$ a positive integer. The $k$-closure $G^{(k)}$ of $G$ is the largest subgroup of $\mathrm{Sym}(\Omega )$, with the same as $G$ o…