The structure of c-decomposable p^w+n-projective abelian p-groups

An Application of Set Theory to ω + n-Totally p ω+n -Projective Primary Abelian Groups

“…Suppose A is an unbounded separable p ω+2 -projective group with the property that every summand of A which is Σ-cyclic must be bounded (an example of which was constructed by Cutler and Missel in [3]). Since any unbounded p ω+1 -projective group has unbounded Σ-cyclic summands, it follows that A is not p ω+1 -projective.…”

Note on elongations of totally projective p-groups by p ω+n -projective p-groups

“…Nevertheless Keef demonstrated in [12] via a concrete counter-example that this is not the case for the p ω+n -projectives provided n > 1; under the additional circumstances on the decomposing structure of the group to be C-decomposable such a similar decomposition is possible (in this aspect the reader can also see [1] and [13]). Even more, Keef illustrated in [12] that there exists a p ω+n -projective group which is a separate strong ω-elongation of a totally projective group by a separable p ω+n -projective group but that is not a direct sum of a separable p ω+n -projective group with a totally projective group.…”

Notes on Essentially Finitely Indecomposable Nonthick Primary Abelian Groups

“…Since G is thick, the epimorphism G → G/C is small, that is, L ⊆ C for some large subgroup L of G. Thus, by Fuchs (1974Fuchs ( /1977, L is a direct sum of cyclic groups and hence, Danchev (2004) applies to show that G is a direct sum of cyclic groups, whence bounded. Accordingly, taking into account an example due to Cutler and Missel (1984) of an unbounded efi p +2 -projective group, we conclude that there is an efi nonthick group (see Dugas and Irwin, 1992 too).…”