The balanced-projective dimension of p-local abelian groups

AbstractBy generalizing Hill's theorem giving a necessary and sufficient condition for an isotype subgroup of a totally projective p-group to be itself totally projective, we are able to give a condition which will determine the balanced-projective dimension of an arbitrary p-local abelian group when that dimension is finite. We rely on our recent third axiom of countability characterization for p-local balanced projectives and are able to carry over almost routinely the arguments given recently by Fuchs and Hill which were used to determine the balanced-projective dimension of an arbitrary abelian p-group. We are then able to prove that the balanced-projective dimension of any countable p-local abelian group and of any p-local Warfieid group is less than or equal to 1