Let $Y,X$ be two sets of size n,m. Let $Y\subset X$. What is the maximal group(in size) $G< Sym(X)$ such that gY=Y imply that $g=1$?
Here since $G<Sym(X)$ G acts on $X$ and thus also on subsets of $X$.
Group not leaving subset invariant
Klim Efremenko
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