Vol. 22, No. 2, 1967

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On quasi-isomorphic invariants of primary groups

Paul Daniel Hill

Vol. 22 (1967), No. 2, 257–265

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.

Mathematical Subject Classification
Primary: 20.30
Received: 10 October 1966
Published: 1 August 1967
Paul Daniel Hill