Elementary algebraic subset

Definition
A subset $$S$$ of a group $$G$$ is termed an elementary algebraic subgroup if there exists a word map $$w:G^n \to G$$ and elements $$g_1,g_2,\dots,g_{n-1}$$ such that:

$$S = \{ x \in G \mid w(g_1,g_2,\dots,g_{n-1},x) = \mbox{identity element of } G \}$$