On extensions of bounded subgroups in Abelian groups

S. S. Gabriyelyan

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 2, page 175-188
  • ISSN: 0010-2628

Abstract

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It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups H of an infinite Abelian group G , for which there is an infinite subgroup G 0 of G containing H such that G 0 has a special decomposition into a direct sum which takes into account the properties of G , and which induces a natural decomposition of H into a direct sum of finite subgroups.

How to cite

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Gabriyelyan, S. S.. "On extensions of bounded subgroups in Abelian groups." Commentationes Mathematicae Universitatis Carolinae 55.2 (2014): 175-188. <http://eudml.org/doc/261851>.

@article{Gabriyelyan2014,
abstract = {It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups $H$ of an infinite Abelian group $G$, for which there is an infinite subgroup $G_0$ of $G$ containing $H$ such that $G_0$ has a special decomposition into a direct sum which takes into account the properties of $G$, and which induces a natural decomposition of $H$ into a direct sum of finite subgroups.},
author = {Gabriyelyan, S. S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Abelian group; bounded group; simple extension; infinite Abelian groups; bounded subgroups; simple extensions; direct sums of subgroups},
language = {eng},
number = {2},
pages = {175-188},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On extensions of bounded subgroups in Abelian groups},
url = {http://eudml.org/doc/261851},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Gabriyelyan, S. S.
TI - On extensions of bounded subgroups in Abelian groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 2
SP - 175
EP - 188
AB - It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups $H$ of an infinite Abelian group $G$, for which there is an infinite subgroup $G_0$ of $G$ containing $H$ such that $G_0$ has a special decomposition into a direct sum which takes into account the properties of $G$, and which induces a natural decomposition of $H$ into a direct sum of finite subgroups.
LA - eng
KW - Abelian group; bounded group; simple extension; infinite Abelian groups; bounded subgroups; simple extensions; direct sums of subgroups
UR - http://eudml.org/doc/261851
ER -

References

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  1. Fuchs L., Abelian Groups, Budapest: Publishing House of the Hungarian Academy of Sciences 1958, Pergamon Press, London, third edition, reprinted 1967. Zbl1265.06054MR0106942
  2. Gabriyelyan S.S., Finitely generated subgroups as a von Neumann radical of an Abelian group, Mat. Stud. 38 (2012), 124–138. MR3057998
  3. Gabriyelyan S.S., Bounded subgroups as a von Neumann radical of an Abelian group, preprint. 
  4. Markov A.A., On free topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 9 (1945), 3–64 (in Russian); English transl. in: Amer. Math. Soc. Transl. (1) 8 (1962), 195–272. MR0012301
  5. Markov A.A., On the existence of periodic connected topological groups, Izv. Akad. Nauk SSSR Ser. Mat. 8 (1944), 225–232 (in Russian); English transl. in: Amer. Math. Soc. Transl. (1) 8 (1962), 186–194. MR0012300
  6. Nienhuys J.W., Constructions of group topologies on abelian groups, Fund. Math. 75 (1972), 101–116. MR0302810

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