Korean Journal of Mathematics

  • 제21권4호
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  • Pages.401-419
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  • 2013
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ON ALMOST n-SIMPLY PRESENTED ABELIAN p-GROUPS

  • Danchev, Peter V. (Department of Mathematics, Plovdiv University)
  • 투고 : 2013.08.10
  • 심사 : 2013.11.28
  • 발행 : 2013.12.30
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초록

Let $n{\geq}0$ be an arbitrary integer. We define the class of almost n-simply presented abelian p-groups. It naturally strengthens all the notions of almost simply presented groups introduced by Hill and Ullery in Czechoslovak Math. J. (1996), n-simply presented p-groups defined by the present author and Keef in Houston J. Math. (2012), and almost ${\omega}_1-p^{{\omega}+n}$-projective groups developed by the same author in an upcoming publication [3]. Some comprehensive characterizations of the new concept are established such as Nunke-esque results as well as results on direct summands and ${\omega}_1$-bijections.

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참고문헌

  1. B. Balof and P. Keef, Invariants on primary abelian groups and a problem of Nunke, Note Mat. 29 (2) (2009), 83-114.
  2. P. Danchev, On extensions of primary almost totally projective groups, Math. Bohemica 133 (2) (2008), 149-155.
  3. P. Danchev, On almost ${\omega}_1$-$p^{{\omega}+n}$ projective abelian p-groups, accepted.
  4. P. Danchev, On ${\omega}_1$-n-simply presented abelian p-groups, submitted.
  5. P. Danchev and P. Keef, Generalized Wallace theorems, Math. Scand. 104 (1) (2009), 33-50. https://doi.org/10.7146/math.scand.a-15083
  6. P. Danchev and P. Keef, Nice elongations of primary abelian groups, Publ. Mat. 54 (2) (2010), 317-339. https://doi.org/10.5565/PUBLMAT_54210_02
  7. P. Danchev and P. Keef, An application of set theory to ${\omega}$+n -totally $p^{{\omega}+n}$ projective primary abelian groups, Mediterr. J. Math. (4) 8 (2011), 525-542. https://doi.org/10.1007/s00009-010-0088-2
  8. L. Fuchs, Infinite Abelian Groups, volumes I and II, Acad. Press, New York and London, 1970 and 1973.
  9. P. Griffith, Infinite Abelian Group Theory, The University of Chicago Press, Chicago-London, 1970.
  10. P. Hill, Almost coproducts of finite cyclic groups, Comment. Math. Univ. Carolin. 36 (4) (1995), 795-804.
  11. P. Hill and W. Ullery, Isotype separable subgroups of totally projective groups, Abelian Groups and Modules, Proc. Padova Conf., Padova 1994, Kluwer Acad. Publ. 343 (1995), 291-300.
  12. P. Hill and W. Ullery, Almost totally projective groups, Czechoslovak Math. J. 46 (2) (1996), 249-258.
  13. P. Keef, On ${\omega}_1$-$p^{{\omega}+n}$-projective primary abelian groups, J. Algebra Numb. Th. Acad. 1 (1) (2010), 41-75.
  14. P. Keef and P. Danchev, On n-simply presented primary abelian groups, Houston J. Math. 38 (4) (2012), 1027-1050.
  15. P. Keef and P. Danchev, On m, n-balanced projective and m, n-totally pojective primary abelian groups, J. Korean Math. Soc. 50 (2) (2013), 307-330. https://doi.org/10.4134/JKMS.2013.50.2.307