Generating set of a group

Common card · No. 450290

In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses. In other words, if S {\displaystyle S} is a subset of a group G {\displaystyle G} , then ⟨ S ⟩ {\displaystyle \langle S\rangle } , the subgroup generated by S {\displaystyle S} , is the smallest subgroup of G {\displaystyle G} containing every element of S {\displaystyle S} , which is equal to the intersection over all subgroups containing the elements of S {\displaystyle S} ; equivalently, ⟨ S ⟩...

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