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## Main Question or Discussion Point

Hi, I need some help with this problem:

Let H be a subgroup of an arbitary group G. Prove H is normal iff it has the following property: For all a,b, in G, ab is in H iff ab is in H.

Let H be a subgroup of an arbitary group G. Prove H is normal iff it has the following property: For all a,b, in G, ab is in H iff ab is in H.