@@How this problem works
@@FP

@@ABELIAN

\ni In order to see if an element generates a pure subgroup, we compute
the primary decomposition of the element. If there are both infinite
cyclic and finite cyclic factors involved, then the element does
not generate a pure subgroup. If there are only infinite cyclic
groups involved and the group is torsion-free, then the subgroup
generated by the element is pure only if it is not a proper power.
If no infinite cyclic factors are involved, then the subgroup 
generated by the element is pure only if the p-heights of its  p-primary 
components are always 1 in each sylow p-subgroup.

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

@@NILPOTENT

@@FREE

@@AP_FREE

@@AP_FREE_CYCLIC

@@SMALL_CANCELLATION

@@ONE_RELATOR


@@How this problem works

There is no documentation for this problem yet.

