If (G,*) is group and each subgroups of (G,*) is normal subgroups then (G,*) is abelian group.
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- Find a subset of Z that is closed under addition but is not subgroup of the additive group Z.12. Find all normal subgroups of the quaternion group.27. a. Show that a cyclic group of order has a cyclic group of order as a homomorphic image. b. Show that a cyclic group of order has a cyclic group of order as a homomorphic image.