Abelianness is subgroup-closed

Statement
Any subgroup of an abelian group is an abelian group.

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