| Axiom | Statement |
|---|---|
| Associativity | \(\forall a,b,c \in G, (a \cdot b) \cdot c = a \cdot (b \cdot c)\) |
| Identity | \(\exists e \in G, \forall a \in G, e \cdot a = a \cdot e = a\) |
| Inverse | \(\forall a \in G, \exists b \in G, a \cdot b = b \cdot a = e\)1 |
\(b\) is commonly denoted \(a^{-1}\), and \(e\) is the identity.↩︎