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