Subgroup of Abelian Group is Abelian

Theorem

A subgroup of an abelian group is itself abelian.

Proof

Follows directly from Restriction of Commutative Operation is Commutative.

$\blacksquare$

Sources

• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 5.2$. Subgroups: Example $89$