Definition:Group Axioms/Right

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Definition

A group is an algebraic structure $\struct {G, \circ}$ which satisfies the following four conditions:

\((G 0)\)   $:$   Closure Axiom      \(\displaystyle \forall a, b \in G:\) \(\displaystyle a \circ b \in G \)             
\((G 1)\)   $:$   Associativity Axiom      \(\displaystyle \forall a, b, c \in G:\) \(\displaystyle a \circ \paren {b \circ c} = \paren {a \circ b} \circ c \)             
\((G_R 2)\)   $:$   Right Identity Axiom      \(\displaystyle \exists e \in G: \forall a \in G:\) \(\displaystyle a \circ e = a \)             
\((G_R 3)\)   $:$   Right Inverse Axiom      \(\displaystyle \forall a \in G: \exists b \in G:\) \(\displaystyle a \circ b = e \)             


Also see


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