Some generalizations of torsion-free Crawley groups

Title:

Some generalizations of torsion-free Crawley groups

Creator:

Goldsmith, Brendan, Karimi, Fatemeh, and Aghdam, Ahad Mehdizahed

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:39f5f86f-8b10-42b6-a6fc-b2781ec6d5ac
uuid:39f5f86f-8b10-42b6-a6fc-b2781ec6d5ac

Subject:

Abelian group, Crawley group, weak Crawley group, and Erdős group

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

n 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

819-831

Source:

Czechoslovak Mathematical Journal | 2013 Volume:63 | Number:3

Harvested from:

CDK

Metadata only:

false