Talk:Opposite group

I think that in "Group Action" section $$\rho: G \to \mathrm{Aut}(X)$$ should be replaced by $$\rho: G \to \mathrm{Sym}(X)$$, because there is not (necessarily) a group structure/operation on X. Also in the "Group Action" article the talk is about induced permutations, thus symmetric group. But I'm not an expert to correct it.