If Y is a subset of X, then G ⋅ Y denotes the set { g ⋅ y : g ∈ G and y ∈ Y }. The subset Y is said to be invariant under G if G ⋅ Y = Y (which is equivalent G ⋅ Y ⊆ Y). In that case, G also operates on Y by restricting the action to Y. The subset Y is called fixed under G if g ⋅ y = y for all g in G and all y in Y. Every subset that is fixed under G is also invariant under G, but not conversely.