Group in Math , Definitions and Examples-Double Math:-

Definition: A non-empty set G having binary operation “*” (say) is called group in math if it satisfies the following axioms:

i.e, $a\ast b\in G\;\;\;\;\;\;\;\forall\;a,b\in G$

$(a\ast b)\ast c=a\ast(b\ast c)\;\;\;\;\;\;:\;\forall\;a,b,c\in G$ .

There is identity element e in G such that

$a\ast e=e\ast a=a\;\;\;\;\;\;\;\;\forall\;a\in G$ .

For each $a\in G$ , there is an $a^{-1}\in\;G$ such that

you can also check semi group and monoid