About: Abelian groups with a minimal generating set     Goto   Sponge   NotDistinct   Permalink

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Description
  • We study the existence of minimal generating sets in abelian groups. We prove that abelian groups with minimal generating sets are closed neither under quotients, nor under subgroups, nor under infinite products. We give necessary and sufficient conditions for existence of a minimal generating set providing that the abelian group is uncountable, torsion, or torsion-free completely decomposable.
  • We study the existence of minimal generating sets in abelian groups. We prove that abelian groups with minimal generating sets are closed neither under quotients, nor under subgroups, nor under infinite products. We give necessary and sufficient conditions for existence of a minimal generating set providing that the abelian group is uncountable, torsion, or torsion-free completely decomposable. (en)
Title
  • Abelian groups with a minimal generating set
  • Abelian groups with a minimal generating set (en)
skos:prefLabel
  • Abelian groups with a minimal generating set
  • Abelian groups with a minimal generating set (en)
skos:notation
  • RIV/00216208:11320/10:10050566!RIV11-GA0-11320___
http://linked.open...avai/riv/aktivita
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  • P(GA201/06/0510), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 2
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  • 245096
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  • RIV/00216208:11320/10:10050566
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  • set; generating; minimal; with; groups; Abelian (en)
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http://linked.open...odStatuVydavatele
  • ZA - Jihoafrická republika
http://linked.open...ontrolniKodProRIV
  • [AF4C0DEC2B37]
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  • Quaestiones Mathematicae
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  • 33
http://linked.open...iv/tvurceVysledku
  • Růžička, Pavel
http://linked.open...ain/vavai/riv/wos
  • 000279634500002
http://linked.open...n/vavai/riv/zamer
issn
  • 1607-3606
number of pages
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  • 11320
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