Some generalizations of torsion-free Crawley groups

Goldsmith, Brendan, Karimi, Fatemeh, and Aghdam, Ahad Mehdizadeh. "Some generalizations of torsion-free Crawley groups." Czechoslovak Mathematical Journal 63.3 (2013): 819-831. <http://eudml.org/doc/260728>.

@article{Goldsmith2013,
abstract = {In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group $G$ is said to be an Erdős group if for any pair of isomorphic pure subgroups $H,K$ with $G/H \cong G/K$, there is an automorphism of $G$ mapping $H$ onto $K$; it is said to be a weak Crawley group if for any pair $H, K$ of isomorphic dense maximal pure subgroups, there is an automorphism mapping $H$ onto $K$. We show that these classes are extensive and pay attention to the relationship of the Baer-Specker group to these classes. In particular, we show that the class of Crawley groups is strictly contained in the class of weak Crawley groups and that the class of Erdős groups is strictly contained in the class of weak Crawley groups.},
author = {Goldsmith, Brendan, Karimi, Fatemeh, Aghdam, Ahad Mehdizadeh},
journal = {Czechoslovak Mathematical Journal},
keywords = {Abelian group; Crawley group; weak Crawley group; Erdős group; torsion-free Abelian groups; weak Crawley groups; Erdős groups; pure subgroups; automorphisms},
language = {eng},
number = {3},
pages = {819-831},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some generalizations of torsion-free Crawley groups},
url = {http://eudml.org/doc/260728},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Goldsmith, Brendan
AU - Karimi, Fatemeh
AU - Aghdam, Ahad Mehdizadeh
TI - Some generalizations of torsion-free Crawley groups
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 819
EP - 831
AB - In this paper we investigate two new classes of torsion-free Abelian groups which arise in a natural way from the notion of a torsion-free Crawley group. A group $G$ is said to be an Erdős group if for any pair of isomorphic pure subgroups $H,K$ with $G/H \cong G/K$, there is an automorphism of $G$ mapping $H$ onto $K$; it is said to be a weak Crawley group if for any pair $H, K$ of isomorphic dense maximal pure subgroups, there is an automorphism mapping $H$ onto $K$. We show that these classes are extensive and pay attention to the relationship of the Baer-Specker group to these classes. In particular, we show that the class of Crawley groups is strictly contained in the class of weak Crawley groups and that the class of Erdős groups is strictly contained in the class of weak Crawley groups.
LA - eng
KW - Abelian group; Crawley group; weak Crawley group; Erdős group; torsion-free Abelian groups; weak Crawley groups; Erdős groups; pure subgroups; automorphisms
UR - http://eudml.org/doc/260728
ER -