@@How this problem works
@@FP
@@ABELIAN

\ni The torsion-free rank of a subgroup is the number of
infinite cyclic factors in a decomposition of that subgroup
into a direct product of  cyclic groups.

\ni For a general discussion see 
@General_abelian_groups@General_abelian_groups::General discussion@
@@AP_FREE

@@AP_FREE_CYCLIC

@@SMALL_CANCELLATION

@@ONE_RELATOR
