Pure subgroups

Bican, 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 -