1. Group

1. Basic Concept

(1) Group

(G, ·) group $⟺$

• ① 结合律: $\mathrm{\forall }a,b,c\in G,a·(b·c)=(a·b)·c$
• ② 单位元: $\mathrm{\exists }e\in G,\mathrm{\forall }a\in G,a·e=e·a=a$
• ③ 逆元: $\mathrm{\forall }a\in G,\mathrm{\exists }{a}^{-1}\in G,a·a^{-1}=a^{-1}·a=e$