@article {IOPORT.05836896,
    author       = {Ku, Cheng Yeaw and Wong, Kok Bin},
    title        = {The group marriage problem.},
    year         = {2011},
    journal      = {Journal of Combinatorial Theory. Series A},
    volume       = {118},
    number       = {2},
    issn         = {0097-3165},
    pages        = {672-680},
    publisher    = {Elsevier Science (Academic Press), San Diego, CA},
    doi          = {10.1016/j.jcta.2010.08.002},
    abstract     = {Summary: Let $G$ be a permutation group acting on $[n]=\{1,\dots,n\}$ and $\cal V=\{V_i:i=1,\dots,n\}$ be a system of $n$ subsets of $[n]$. When is there an element $g\in G$ so that $g(i)\in V_i$ for each $i\in [n]$? If such a $g$ exists, we say that $G$ has a $G$-marriage subject to $\cal V$. An obvious necessary condition is the `orbit condition': for any nonempty subset $Y$ of $[n]$, there is an element $g\in G$ such that the image of $Y$ under $g$ is contained in $\bigcup_{y\in Y}V_y$. Keevash observed that the orbit condition is sufficient when $G$ is the symmetric group $S_n$; this is in fact equivalent to the celebrated Hall's Marriage Theorem. We prove that the orbit condition is sufficient if and only if $G$ is a direct product of symmetric groups. We extend the notion of orbit condition to that of $k$-orbit condition and prove that if $G$ is the cyclic group $C_n$ where $n\ge 4$ or $G$ acts 2-transitively on $[n]$, then $G$ satisfies the $(n-1)$-orbit condition subject to $\cal V$ if and only if $G$ has a $G$-marriage subject to $\cal V$.},
    identifier   = {05836896},
}