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# System prepended metadata

title: Finite groups

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# Finite groups 

A finite group is a set $G$ equipped with a binary operation $\mu\colon G\times G \to G$ such that 

- $\mu$ is associative : $\mu(\mu(x,y),z) = \mu(x,\mu(y,z))$ for all $x$, $y$, and $z$ in $G$. 

- there is a neutral element $e\in G$ for the operation $\mu$ 
   $\mu(x,e) = \mu(e,x) = x$ for all $x\in G$. 
   
   Notice that this neutral element is unique as soon as it exists. 
   
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