# Pure subgroups

Mathematica Bohemica (2001)

- Volume: 126, Issue: 3, page 649-652
- ISSN: 0862-7959

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topBican, Ladislav. "Pure subgroups." Mathematica Bohemica 126.3 (2001): 649-652. <http://eudml.org/doc/248863>.

@article{Bican2001,

abstract = {Let $\lambda $ be an infinite cardinal. Set $\lambda _0=\lambda $, define $\lambda _\{i+1\}=2^\{\lambda _i\}$ for every $i=0,1,\dots $, take $\mu $ as the first cardinal with $\lambda _i<\mu $, $i=0,1,\dots $ and put $\kappa = (\mu ^\{\aleph _0\})^+$. If $F$ is a torsion-free group of cardinality at least $\kappa $ and $K$ is its subgroup such that $F/K$ is torsion and $|F/K|\le \lambda $, then $K$ contains a non-zero subgroup pure in $F$. This generalizes the result from a previous paper dealing with $F/K$$p$-primary.},

author = {Bican, Ladislav},

journal = {Mathematica Bohemica},

keywords = {torsion-free abelian groups; pure subgroup; $P$-pure subgroup; torsion-free Abelian groups; pure subgroups; -pure subgroups},

language = {eng},

number = {3},

pages = {649-652},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Pure subgroups},

url = {http://eudml.org/doc/248863},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Bican, Ladislav

TI - Pure subgroups

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 3

SP - 649

EP - 652

AB - Let $\lambda $ be an infinite cardinal. Set $\lambda _0=\lambda $, define $\lambda _{i+1}=2^{\lambda _i}$ for every $i=0,1,\dots $, take $\mu $ as the first cardinal with $\lambda _i<\mu $, $i=0,1,\dots $ and put $\kappa = (\mu ^{\aleph _0})^+$. If $F$ is a torsion-free group of cardinality at least $\kappa $ and $K$ is its subgroup such that $F/K$ is torsion and $|F/K|\le \lambda $, then $K$ contains a non-zero subgroup pure in $F$. This generalizes the result from a previous paper dealing with $F/K$$p$-primary.

LA - eng

KW - torsion-free abelian groups; pure subgroup; $P$-pure subgroup; torsion-free Abelian groups; pure subgroups; -pure subgroups

UR - http://eudml.org/doc/248863

ER -

## References

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- Flat Covers of Modules, Lecture Notes in Mathematics 1634, Springer, Berlin, 1996. (1996) Zbl0860.16002MR1438789

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