group

A set $G$ with a single operation - multiplication $\cdot :G\times G\to G$ that follows the group axioms:

• Associativity For $a,b,c\in G$ $a\cdot (b\cdot c)=(a\cdot b)\cdot c$
• Identity element There exists an element $e\in G$ such that $eg=ge=g$ for all $g\in G$.
• Inverse element For every $g\in G$, $\exists g^{-}1$ such that $g{g}^{-1}=g^{-1}g=e$.

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