On Topologies on the Group $(\Z_p)^{\N}$
  It is proved that, on any Abelian group of infinite cardinality ${\bf m}$, there exist precisely $2^{2^{\bf m}}$ nonequivalent bounded Hausdorff group topologies. Under the continuum hypothesis, the number of nonequivalent compact and locally compact Hausdorff group topologies on the group $(\Z_p)^{\N}$ is determined. 
I.K. Babenko and S.A. Bogatyi
math.GR