suppose that $G<S_n$ is a subgroup of permutations of $\{1,...,n\}$ with this property that for every $e\neq g\in G$ there exist exactly one $k\in \{1,...,n\}$ such that $g.k=k$. prove that there exist one $k\in \{1,...,n\}$ such that for every $g\in G$ we have $g.k=k$.(20 points)