RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Vladikavkaz. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Vladikavkaz. Mat. Zh., 2007, Volume 9, Number 1, Pages 30–37 (Mi vmj85)  

This article is cited in 3 scientific papers (total in 3 papers)

A note on weakly $\aleph_1$-separable $p$-groups

P. V. Danchev

Plovdiv State University Paissii Hilendarski, Plovdiv, Bulgaria

Abstract: It is well-known by Hill-Griffith that there exist $\aleph_1$-separable $p$-primary groups which are not direct sums of cycles. A problem of challenging interest, mainly due to Hill (Rocky Mount. J. Math., 1971), is under what extra circumstances on the group structure this holds untrue, that is every $\aleph_1$-separable $p$-group is a direct sum of cyclic groups. We prove here that any weakly $\aleph_1$-separable $p$-group of cardinality not exceeding $\aleph_1$ is quasi-complete precisely when it is a bounded direct sum of cycles, thus partly answering the posed question in the affirmative.

Key words: weakly $\aleph_1$-separable groups, quasi-complete groups, torsion-complete groups, bounded groups.

Full text: PDF file (142 kB)
References: PDF file   HTML file

Bibliographic databases:
UDC: 512.742
MSC: 20K 10
Received: 03.07.2006
Language:

Citation: P. V. Danchev, “A note on weakly $\aleph_1$-separable $p$-groups”, Vladikavkaz. Mat. Zh., 9:1 (2007), 30–37

Citation in format AMSBIB
\Bibitem{Dan07}
\by P.~V.~Danchev
\paper A note on weakly $\aleph_1$-separable $p$-groups
\jour Vladikavkaz. Mat. Zh.
\yr 2007
\vol 9
\issue 1
\pages 30--37
\mathnet{http://mi.mathnet.ru/vmj85}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2434621}
\elib{http://elibrary.ru/item.asp?id=11620327}


Linking options:
  • http://mi.mathnet.ru/eng/vmj85
  • http://mi.mathnet.ru/eng/vmj/v9/i1/p30

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. V. Danchev, “Quasi-complete Q-groups are bounded”, Vladikavk. matem. zhurn., 10:1 (2008), 24–26  mathnet  mathscinet
    2. P. V. Danchev, “Weakly $\aleph_1$-separable quasi-complete abelian $p$-groups are bounded”, Vladikavk. matem. zhurn., 11:3 (2009), 8–9  mathnet  mathscinet  elib
    3. Danchev P.V., “On the algebraically compact $\aleph_1$-embedding abelian groups”, Analele Stiintifice Ale Universitatii Al i Cuza Din Iasi-Serie Noua-Matematica, 55:1 (2009), 187–192  mathscinet  zmath  isi
  • Number of views:
    This page:169
    Full text:63
    References:32
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020