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Prove that if a group $G$ is generated by all cyclic subnormal subgroups, then every cyclic subgroup is subnormal

I have already found two definitions for a Baer group.

  1. $G$ is a Baer group if it is generated by all cyclic subnormal subgroups.

  2. $G$ is a Baer group if every cyclic subgroup is subnormal.

I want to prove the equivalence of the two definitions. Obviously, (2) implies (1). Please help me with the converse.