Two primary groups G and H
are quasi-isomorphic if there exist subgroups G∗ and H∗ of G and H such that G∗
and H∗ are isomorphic and such that G∕G∗ and H∕H∗ are bounded. The
paper is concerned with properties, of primary groups, that are invariant
under the relation of quasi-isomorphism. In the final section, a condition is
given which is necessary and sufficient in order that the primary groups G
and H be quasi-isomorphic in case G and H are both direct sums of closed
groups.
The main result of the paper is that quasi-isomorphism commutes with direct
decomposition for the class of primary groups whose first Ulm factors are direct sums
of countable groups.
