Abstract
A p-primary abelian group G is called almost totally projective if it has a collection C of nice subgroups with the following properties: (0) 0 ∈ C, (1) C is closed with respect to unions of ascending chains, and (2) every countable subgroup of G is contained in a countable subgroup from C. Observe that this is a generalization of the Axiom 3 characterization of totally projective groups. In this paper, we show that the isotype subgroups of a totally projective group which are almost totally projective are precisely those that are separable. From this characterization it follows that every balanced subgroup of a totally projective group is almost totally projective. It is also shown that the class of almost totally projective groups is closed under the formation of countable extensions. Finally, in some special cases we settle the question of whether a direct summand of an almost totally projective group is again almost totally projective.
Supported by NSF grant DMS 92-08199
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© 1995 Springer Science+Business Media Dordrecht
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Hill, P., Ullery, W. (1995). Isotype Separable Subgroups of Totally Projective Groups. In: Facchini, A., Menini, C. (eds) Abelian Groups and Modules. Mathematics and Its Applications, vol 343. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0443-2_24
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DOI: https://doi.org/10.1007/978-94-011-0443-2_24
Publisher Name: Springer, Dordrecht
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