On the structure of abelian $p$-groups

Paul Hill
1985 Transactions of the American Mathematical Society  
A new kind of abelian p-gioup, called an A -group, is introduced. This class contains the totally projective groups and Warfield's S-groups as special cases. It also contains the V-groups recently classified by the author. These more general groups are classified by cardinal (numerical) invariants which include, but are not limited to, the Ulm-Kaplansky invariants. Thus the existing theory, as well as the classification, of certain abelian ^-groups is once again generalized. Having classified
more » ... -groups (by means of a uniqueness and corresponding existence theorem) we can successfully study their structure and special properties. Such a study is initiated in the last section of the paper.
doi:10.1090/s0002-9947-1985-0776390-3 fatcat:b65yrhodsrdwhgwusuc6zkbx3a