Group Marriage Problem

Cheng Yeaw Ku, Kok Bin Wong

Let $G$ be a permutation group acting on $[n]=\{1,...,n\}$ and $\mathcal{V}=\{V_i:i=1,...,n\}$ be a system of $n$ subsets of $[n]$. When is there an element $g\in G$ so tha…