Title: | On countable extensions of primary abelian groups (English) |

Author: | Danchev, P. V. |

Language: | English |

Journal: | Archivum Mathematicum |

ISSN: | 0044-8753 (print) |

ISSN: | 1212-5059 (online) |

Volume: | 43 |

Issue: | 1 |

Year: | 2007 |

Pages: | 61-66 |

Summary lang: | English |

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Category: | math |

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Summary: | It is proved that if $A$ is an abelian $p$-group with a pure subgroup $G$ so that $A/G$ is at most countable and $G$ is either $p^{\omega +n}$-totally projective or $p^{\omega +n}$-summable, then $A$ is either $p^{\omega +n}$-totally projective or $p^{\omega +n}$-summable as well. Moreover, if in addition $G$ is nice in $A$, then $G$ being either strongly $p^{\omega +n}$-totally projective or strongly $p^{\omega +n}$-summable implies that so is $A$. This generalizes a classical result of Wallace (J. Algebra, 1971) for totally projective $p$-groups as well as continues our recent investigations in (Arch. Math. (Brno), 2005 and 2006). Some other related results are also established. (English) |

Keyword: | countable quotient groups |

Keyword: | $\omega $-elongations |

Keyword: | $p^{\omega +n}$-totally projective groups |

Keyword: | $p^{\omega +n}$-summable groups |

MSC: | 20K10 |

MSC: | 20K15 |

idZBL: | Zbl 1156.20044 |

idMR: | MR2310125 |

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Date available: | 2008-06-06T22:50:32Z |

Last updated: | 2012-05-10 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/108050 |

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Reference: | [1] Benabdallah K., Eisenstadt B., Irwin J., Poluianov E.: The structure of large subgroups of primary abelian groups.Acta Math. Acad. Sci. Hungar. 21 (3-4) (1970), 421–435. Zbl 0215.39804, MR 0276328 |

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Reference: | [4] Danchev P.: Countable extensions of torsion abelian groups.Arch. Math. (Brno) 41 (3) (2005), 265–272. Zbl 1114.20030, MR 2188382 |

Reference: | [5] Danchev P.: A note on the countable extensions of separable $p^{\omega +n}$-projective abelian $p$-groups.Arch. Math. (Brno) 42 (3) (2006), 251–254. MR 2260384 |

Reference: | [6] Danchev P.: Generalized Wallace theorems.submitted. Zbl 1169.20029 |

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Reference: | [12] Nunke R.: Homology and direct sums of countable abelian groups.Math. Z. 101 (3) (1967), 182–212. Zbl 0173.02401, MR 0218452 |

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