  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.
