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.