Noetherianness is subgroup-closed

This article gives the statement, and possibly proof, of a group property (i.e., Noetherian group) satisfying a group metaproperty (i.e., subgroup-closed group property)
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Statement

Any subgroup of a Noetherian group is Noetherian group.

Related facts

Similar facts

• Noetherianness is quotient-closed
• Noetherianness is extenion-closed
• Artinianness is subgroup-closed

Opposite facts

• Finitely generated not implies Noetherian shows that a subgroup of a finitely generated group need not be finitely generated.