Group

Tuple $(G,\times )$ where $\times :G\times G\to G$ is a binary operation where:

1. We have an identity: $\exists e\in G:\forall g\in G,eg=ge=g$
2. We have inverses: $\forall g\in G\exists g^{-1}:g{g}^{-1}=g^{-1}g=e$
3. We have associativity: $(g_1{g}_2)g_3=g_1(g_2{g}_3)\forall g_1,g_2,g_3\in G$