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CHARACTERIZATION OF ABELIAN GROUPS WITH A MINIMAL GENERATING SET

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10317275" target="_blank" >RIV/00216208:11320/15:10317275 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.2989/16073606.2014.981704" target="_blank" >http://dx.doi.org/10.2989/16073606.2014.981704</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.2989/16073606.2014.981704" target="_blank" >10.2989/16073606.2014.981704</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    CHARACTERIZATION OF ABELIAN GROUPS WITH A MINIMAL GENERATING SET

  • Original language description

    We characterize Abelian groups with a minimal generating set: Let tau A denote the maximal torsion subgroup of A. An infinitely generated Abelian group A of cardinality x has a minimal generating set iff at least one of the following conditions is satisfied: 1. dim(A/pA) = dim(A/qA) = x for at least two different primes p, q. 2. dim(tau A/p tau A) = x for some prime number p. 3. Sigma{dim(A/(pA + B)) vertical bar dim(A/(pA + B)) < x} = x for every finitely generated subgroup B of A. Moreover, if the group A is uncountable, property (3) can be simplified to (3') Sigma{dim(A/pA) vertical bar dim(A/pA) < x} = x, and if the cardinality of the group A has uncountable cofinality, then A has a minimal generating set iff any of properties (1) and (2) is satisfied.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GA201%2F09%2F0816" target="_blank" >GA201/09/0816: Algebraic Methods in the Representation Theory (Approximations, Realizations, and Constraints)</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2015

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Quaestiones Mathematicae

  • ISSN

    1607-3606

  • e-ISSN

  • Volume of the periodical

    38

  • Issue of the periodical within the volume

    1

  • Country of publishing house

    ZA - SOUTH AFRICA

  • Number of pages

    18

  • Pages from-to

    103-120

  • UT code for WoS article

    000352805800008

  • EID of the result in the Scopus database

    2-s2.0-84937218461