Every subgroup of an abelian group is ?||Can a non-Abelian group have a normal subgroup?

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CONVERSE OF "IN AN ABELIAN GROUP ALL THE SUBGROUPS ARE NORMAL" CONVERSE OF "IN AN ABELIAN GROUP ALL THE SUBGROUPS ARE NORMAL"
Prove that every subgroup of an abelian group is normal . Prove that every subgroup of an abelian group is normal .
Every Subgroup of an Abelian Group is Normal Proof Every Subgroup of an Abelian Group is Normal Proof
A non-abelian group all of whose subgroups are normal (Example of a Hamiltonian group) A non-abelian group all of whose subgroups are normal (Example of a Hamiltonian group)
Every subgroup of an abelian group is normal Every subgroup of an abelian group is normal
Every subgroup of an abelian group is normal. Every subgroup of an abelian group is normal.
An Example of a non-Normal subgroup of a non-Abelian Group An Example of a non-Normal subgroup of a non-Abelian Group
Every subgroup of an Abelian Group is Normal - Chapter 6 - Lecture 4 Every subgroup of an Abelian Group is Normal - Chapter 6 - Lecture 4