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The balanced-projective dimension of Abelian p-groups. (English) Zbl 0602.20047
A subgroup N of a p-primary abelian group M is isotype if $$p^{\alpha}M\cap N=p^{\alpha}N$$ for all ordinals $$\alpha$$, and it is nice if $$(p^{\alpha}M+N)/N=p^{\alpha}(M/N)$$ for all $$\alpha$$. If N is both isotype and nice in M, it is said to be balanced in M, and the corresponding exact sequence $$0\to N\to M\to M/N\to 0$$ is called balanced-exact. The category of balanced-exact sequences has enough projectives; these are the totally projective p-groups. The balanced- projective dimension of a p-group M is defined in the usual fashion, using balanced totally projective resolutions. The balanced-projective dimension of a p-group is determined by a structural property which generalizes Hill’s third axiom of countability.
Reviewer: K.Faltings

##### MSC:
 20K10 Torsion groups, primary groups and generalized primary groups 20K27 Subgroups of abelian groups 20K40 Homological and categorical methods for abelian groups
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