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Normal Subgroups

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Eli
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#1

A subgroup of a group is said to be a normal subgroup of if for all
and .

We use the notation to signify that is a normal subgroup of .

Claim (Lemma)

Every subgroup of an abelian group is a normal subgroup

Proof

Let be a subgroup of an abelian group .

Then,
.

So, for all and , where is the identiy element, the result holds.
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