# MathGloss/G/Group

< MathGloss‎ | G
Template:Group

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Definition
 Group Let $G$ be a non empty set with binary operation $+$. G is said to be a Group if the following conditions are satisfied: $G$ is closed with respect to $+$ i.e. if $a,b\in G \Rightarrow a+b\in G$ Existance of Identity element i.e.Ther exists $e\in G$ such that for any $a\in G, a+e=a=e+a$ Existance of Inverse i.e. for any $a\in G,$ there exists $b\in G$ such that $a+b=e=b+a$

## Examples

$\Re$ Set of real numbers form a Group with respect to addition"+".