Finite abelian group

Symbol-free definition
A finite abelian group is a group satisfying the following equivalent conditions:


 * 1) It is both finite and abelian.
 * 2) It is isomorphic to a direct product of finitely many finite cyclic groups.
 * 3) It is isomorphic to a direct product of abelian groups of prime power order.
 * 4) It is isomorphic to a direct product of cyclic groups of prime power order.