The nice basis rank of a primary abelian group

Peter Danchev; Patrick Keef

doi:10.1556/sscmath.48.2011.2.1168

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Studia Scientiarum Mathematicarum Hungarica

Volume/Issue:: Volume 48: Issue 2

The nice basis rank of a primary abelian group

Authors:

Peter Danchev

Peter Danchev Plovdiv University “P. Hilendarski” Department of Mathematics Plovdiv 4000 Bulgaria

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and

Patrick Keef

Patrick Keef Whitman College Department of Mathematics Walla Walla WA 99362 USA

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Pages:: 247–256

Online Publication Date:: 09 Jun 2011

Publication Date:: 01 Jun 2011

Article Category:: Journal Article

DOI:: https://doi.org/10.1556/sscmath.48.2011.2.1168

Keywords:: Primary 20K10; Abelian groups; nice bases; divisible hull; ranks; nice basis rank

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An abelian p-group G has a nice basis if it is the ascending union of a sequence of nice subgroups, each of which is a direct sum of cyclic groups. It is shown that if G is any group, then G ⊕ D has a nice basis, where D is the divisible hull of p^ωG. This leads to a consideration of the nice basis rank of G, i.e., the smallest rank of a divisible group D such that G ⊕ D has a nice basis. This concept is used to show that there exist a reduced group G and a non-reduced group H, both without a nice basis, such that G ⊕ H has a nice basis

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Studia Scientiarum Mathematicarum Hungarica

Print ISSN:: 0081-6906

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András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics)

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Imre BÁRÁNY (Rényi Institute of Mathematics)
Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
Péter CSIKVÁRI (ELTE, Budapest)
Joshua GREENE (Boston College)
Penny HAXELL (University of Waterloo)
Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
Ron HOLZMAN (Technion, Haifa)
Satoru IWATA (University of Tokyo)
Tibor JORDÁN (ELTE, Budapest)
Roy MESHULAM (Technion, Haifa)
Frédéric MEUNIER (École des Ponts ParisTech)
Márton NASZÓDI (ELTE, Budapest)
Eran NEVO (Hebrew University of Jerusalem)
János PACH (Rényi Institute of Mathematics)
Péter Pál PACH (BME, Budapest)
Andrew SUK (University of California, San Diego)
Zoltán SZABÓ (Princeton University)
Martin TANCER (Charles University, Prague)
Gábor TARDOS (Rényi Institute of Mathematics)
Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
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