Notes on countable extensions of  p ω + n -projectives

Peter Vassilev Danchev

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 1, page 37-40
  • ISSN: 0044-8753

Abstract

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We prove that if G is an Abelian p -group of length not exceeding ω and H is its p ω + n -projective subgroup for n { 0 } such that G / H is countable, then G is also p ω + n -projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).

How to cite

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Danchev, Peter Vassilev. "Notes on countable extensions of $p^{\omega +n}$-projectives." Archivum Mathematicum 044.1 (2008): 37-40. <http://eudml.org/doc/250433>.

@article{Danchev2008,
abstract = {We prove that if $G$ is an Abelian $p$-group of length not exceeding $\omega $ and $H$ is its $p^\{\omega +n\}$-projective subgroup for $n\in \{\mathbb \{N\}\} \cup \lbrace 0\rbrace $ such that $G/H$ is countable, then $G$ is also $p^\{\omega +n\}$-projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).},
author = {Danchev, Peter Vassilev},
journal = {Archivum Mathematicum},
keywords = {abelian groups; countable factor-groups; $p^\{\omega +n\}$-projective groups; Abelian -groups; countable factor-groups; projective -groups},
language = {eng},
number = {1},
pages = {37-40},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Notes on countable extensions of $p^\{\omega +n\}$-projectives},
url = {http://eudml.org/doc/250433},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Danchev, Peter Vassilev
TI - Notes on countable extensions of $p^{\omega +n}$-projectives
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 1
SP - 37
EP - 40
AB - We prove that if $G$ is an Abelian $p$-group of length not exceeding $\omega $ and $H$ is its $p^{\omega +n}$-projective subgroup for $n\in {\mathbb {N}} \cup \lbrace 0\rbrace $ such that $G/H$ is countable, then $G$ is also $p^{\omega +n}$-projective. This enlarges results of ours in (Arch. Math. (Brno), 2005, 2006 and 2007) as well as a classical result due to Wallace (J. Algebra, 1971).
LA - eng
KW - abelian groups; countable factor-groups; $p^{\omega +n}$-projective groups; Abelian -groups; countable factor-groups; projective -groups
UR - http://eudml.org/doc/250433
ER -

References

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  1. Danchev, P., Countable extensions of torsion abelian groups, Arch. Math. (Brno) 41 (3) (2005), 265–272. (2005) Zbl1114.20030MR2188382
  2. Danchev, P., Generalized Dieudonné criterion, Acta Math. Univ. Comenian. 74 (1) (2005), 15–26. (2005) Zbl1111.20045MR2154393
  3. Danchev, P., A note on the countable extensions of separable p ω + n -projective abelian p -groups, Arch. Math. (Brno) 42 (3) (2006), 251–254. (2006) Zbl1152.20045MR2260384
  4. Danchev, P., On countable extensions of primary abelian groups, Arch. Math. (Brno) 43 (1) (2007), 61–66. (2007) Zbl1156.20044MR2310125
  5. Danchev, P., Keef, P., Generalized Wallace theorems, Math. Scand. (to appear). (to appear) MR2498370
  6. Dieudonné, J., Sur les p -groupes abeliens infinis, Portugal. Math. 11 (1) (1952), 1–5. (1952) MR0046356
  7. Fuchs, L., Infinite Abelian Groups, I, II, Mir, Moskva, 1974 and 1977, (in Russian). (1974 and 1977) MR0457533
  8. Fuchs, L., 10.1007/BFb0068194, Lecture Notes in Math. 616 (1977), 158–167. (1977) Zbl0389.15001MR0480700DOI10.1007/BFb0068194
  9. Hill, P., Megibben, C., 10.1090/S0002-9939-1974-0340452-3, Proc. Amer. Math. Soc. 44 (2) (1974), 259–262. (1974) Zbl0292.20050MR0340452DOI10.1090/S0002-9939-1974-0340452-3
  10. Nunke, R., Topics in Abelian Groups, ch. Purity and subfunctors of the identity, pp. 121–171, Scott, Foresman and Co., Chicago, 1963. (1963) MR0169913
  11. Nunke, R., 10.1007/BF01135839, Math. Z. 101 (3) (1967), 182–212. (1967) Zbl0173.02401MR0218452DOI10.1007/BF01135839
  12. Wallace, K., 10.1016/0021-8693(71)90005-6, J. Algebra 17 (4) (1971), 482–488. (1971) Zbl0215.39902MR0272891DOI10.1016/0021-8693(71)90005-6

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