<P> An abelian group is called torsion - free if every non-zero element has infinite order . Several classes of torsion - free abelian groups have been studied extensively: </P> <Ul> <Li> Free abelian groups, i.e. arbitrary direct sums of Z </Li> <Li> Cotorsion and algebraically compact torsion - free groups such as the p - adic integers </Li> <Li> Slender groups </Li> </Ul> <Li> Free abelian groups, i.e. arbitrary direct sums of Z </Li> <Li> Cotorsion and algebraically compact torsion - free groups such as the p - adic integers </Li>

Example of abelian group which is not cyclic