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Removed the deprecated (abstract-algebra) tag - see the tag info: https://mathoverflow.net/tags/abstract-algebra/info (if there are some other suitable tags, choose them instead.)

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edited Aug 2, 2018 at 9:40

Martin Sleziak

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asked Aug 2, 2018 at 7:28

Abbas Jafarzadeh

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.

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

gr.group-theory abstract-algebra