Hokkaido Mathematical Journal

A class of Butler groups and their endomorphism rings

Adolf MADER and Lutz STRÜNGMANN

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Abstract

We study a class of Butler groups of infinite rank, called Hawaiian groups.They are defined as subgroups of a rational vector space and contain parameters that provide for flexibility but are concrete enough to allow for the computation of certain crucial subgroups and quotient groups, to exhibit endomorphisms and describe the endomorphism rings. Most Hawaiian groups are finitely Butler; under stronger assumptions they are not finitely filtered and hence not $B_2$-groups.

Article information

Source
Hokkaido Math. J., Volume 37, Number 2 (2008), 399-425.

Dates
First available in Project Euclid: 21 September 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1253539562

Digital Object Identifier
doi:10.14492/hokmj/1253539562

Mathematical Reviews number (MathSciNet)
MR2415908

Zentralblatt MATH identifier
1148.20039

Subjects
Primary: 20K15: Torsion-free groups, finite rank
Secondary: 20K20: Torsion-free groups, infinite rank 20K35: Extensions 20K40: Homological and categorical methods 18E99: None of the above, but in this section 20J05: Homological methods in group theory

Keywords
torsion-free abelian group of infinite rank Butler group finitely Butler endomorphism ring free direct summand

Citation

MADER, Adolf; STRÜNGMANN, Lutz. A class of Butler groups and their endomorphism rings. Hokkaido Math. J. 37 (2008), no. 2, 399--425. doi:10.14492/hokmj/1253539562. https://projecteuclid.org/euclid.hokmj/1253539562


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