ON STRONGLY AND SEPARABLY ω1-pω+n-PROJECTIVE ABELIAN p-GROUPS

Abstract

Let n ≥ 0 be an arbitrary integer. We prove some results for stronglyn-simply presented abelian p-groups with C-decomposable property, extending classical achievements due to Keef in Commun. Algebra (1990).As applications we define the classes of strongly ω-p ω+n -projective andseparably ω-p ω+n -projective abelian p-groups which are also properlycontained in all ω-p ω+n -projectives, recently defined by Keef in J. Alg.Numb. Th. Acad. (2010). Moreover, some principal descriptions concerning these new objects are obtained as well.

Keywords

• C-decomposable groups, pω+n-projective groups, strongly n-simply presented groups, ω-p ω+n-projective groups, strongly ω-p ω+n-projective groups, boundedsubgroups, countable subgroups, nice subgroups, Ulm subgroups, Ulm factors.

ON STRONGLY AND SEPARABLY ω1-pω+n-PROJECTIVE ABELIAN p-GROUPS

Abstract

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Keywords

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References

1. K. Benabdallah, J. Irwin and M. Rafiq, A core class of abelian p-groups, Sympos. Math. 13 (1974), 195–206.
2. P. Danchev, Countable extensions of torsion abelian groups, Arch. Math. (Brno) 41 (3) (2005), 265–272.
3. P. Danchev, Primary abelian n-Σ-groups revisited, Math. Pannonica 22 (1) (2011), 85–93. P. Danchev, On weakly ω 1 -p ω+n -projective abelian p-groups, J. Indian Math. Soc. 80 (1-4) (2013), 33–46.
4. P. Danchev, On ω 1 -weakly p α -projective abelian p-groups, Bull. Malays. Math. Sci. Soc. 37 (2014).
5. P. Danchev and P. Keef, Generalized Wallace theorems, Math. Scand. 104 (1) (2009), 33–50. P. Danchev and P. Keef, An application of set theory to ω + n-totally p ω+n -projective primary abelian groups, Mediterr. J. Math. 8 (4) (2011), 525–542.
6. P. Danchev and P. Keef, On n-simply presented primary abelian groups, Houston J. Math. 38 (4) (2012), 1027–1050.
7. L. Fuchs, Infinite Abelian Groups, Volumes I and II, Academic Press, New York and London 1970 and 1973.
8. L. Fuchs and J. Irwin, On elongations of totally projective p-groups by p ω+n -projective p-groups, Czechoslovak Math. J. 32 (4) (1982), 511–515.

9. P. Keef, Elongations of totally projective groups and p ω+n -projective abelian groups, Commun. Algebra 18 (12) (1990), 4377–4385.
10. P. Keef, On ω 1 -p ω+n -projective primary abelian groups, J. Alg. Numb. Th. Acad. 1 (1) (2010), 41–75.
11. C. Megibben, On high subgroups, Pac. J. Math. 14 (4) (1964), 1353–1358.
12. R. Nunke, Purity and subfunctors of the identity, Topics in Abelian Groups, Scott, Foresman and Co., 1962, 121–171.