Abelianness is subgroup-closed

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

Any subgroup of an abelian group is an abelian group.

Related facts

Related nice properties of abelian groups

• Abelianness is varietal
• Abelianness is quotient-closed
• Abelianness is direct product-closed
• Abelianness is 2-local

Fractional versions

• Fraction of ordered pairs commuting in subgroup is at least as much as in whole group