# Axiom:Group Axioms/Right

(Redirected from Axiom:Right Group Axioms)
A group is an algebraic structure $\struct {G, \circ}$ which satisfies the following four conditions:
 $(\text G 0)$ $:$ Closure Axiom $\ds \forall a, b \in G:$ $\ds a \circ b \in G$ $(\text G 1)$ $:$ Associativity Axiom $\ds \forall a, b, c \in G:$ $\ds a \circ \paren {b \circ c} = \paren {a \circ b} \circ c$ $(\text G_{\text R} 2)$ $:$ Right Identity Axiom $\ds \exists e \in G: \forall a \in G:$ $\ds a \circ e = a$ $(\text G_{\text R} 3)$ $:$ Right Inverse Axiom $\ds \forall a \in G: \exists b \in G:$ $\ds a \circ b = e$