ScholarLens Back to search
2001•Communications in AlgebraRequires access

THE FULLY INVARIANT EXTENDING PROPERTY FOR ABELIAN GROUPS

Gary F. Birkenmeier, Girgore Călugăreanu, L. Fuchs, H. Pat Goeters

Open publisher page 26 citations

Abstract

An abelian group has the FI-extending property if every fully invariant subgroup is essential in a direct summand. A mixed abelian group has the FI-extending property if and only if it is a direct sum of a torsion and a torsion-free abelian group, both with the FI-extending property. A full characterization is obtained for the abelian groups with the FI-extending property which are either torsion-free of finite rank or torsion.

About this research paper

What this paper is about

An abelian group has the FI-extending property if every fully invariant subgroup is essential in a direct summand. A mixed abelian group has the FI-extending property if and only if it is a direct sum of a torsion and a torsion-free abelian group, both with the FI-extending property. A full characterization is obtained for the abelian groups with the FI-extending property which are either torsion-free of finite rank or torsion.

Why it matters

OpenAlex reports 26 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

An abelian group has the FI-extending property if every fully invariant subgroup is essential in a direct summand. A mixed abelian group has the FI-extending property if and only if it is a direct sum of a torsion and a torsion-free abelian group, both with the FI-extending property. A full characterization is obtained for the abelian groups with the FI-extending property which are either torsion-free of finite rank or torsion.

Key concepts: Rank of an abelian group, Abelian group, Torsion subgroup, Mathematics, Elementary abelian group, Free abelian group, Torsion (gastropod), Pure mathematics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
THE FULLY INVARIANT EXTENDING PROPERTY FOR ABELIAN GROUPS — Research Paper | ScholarLens