Quasi-balanced torsion-free groups

is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced sequences. As an application of our results concerning quasi-balanced sequences, the relationship between the two chains in the quasi-category of torsion-free abelian groups is illuminated.

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Goeters, H. Pat, and Ullery, William. "Quasi-balanced torsion-free groups." Commentationes Mathematicae Universitatis Carolinae 39.3 (1998): 431-443. <http://eudml.org/doc/248239>.

@article{Goeters1998,
abstract = {An exact sequence $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence \[ 0\rightarrow \mathbf \{Q\}\otimes \operatorname\{Hom\}(X,A)\rightarrow \mathbf \{Q\}\otimes \operatorname\{Hom\}(X,B) \rightarrow \mathbf \{Q\}\otimes \operatorname\{Hom\}(X,C)\rightarrow 0 \] is exact for all rank-1 torsion-free abelian groups $X$. This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced sequences. As an application of our results concerning quasi-balanced sequences, the relationship between the two chains in the quasi-category of torsion-free abelian groups is illuminated.},
author = {Goeters, H. Pat, Ullery, William},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasi-balanced; almost balanced; Kravchenko classes; quasi-balanced subgroups; almost balanced subgroups; Kravchenko classes; almost completely decomposable groups; torsion-free Abelian groups of finite rank; almost balanced exact sequences},
language = {eng},
number = {3},
pages = {431-443},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quasi-balanced torsion-free groups},
url = {http://eudml.org/doc/248239},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Goeters, H. Pat
AU - Ullery, William
TI - Quasi-balanced torsion-free groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 3
SP - 431
EP - 443
AB - An exact sequence $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence \[ 0\rightarrow \mathbf {Q}\otimes \operatorname{Hom}(X,A)\rightarrow \mathbf {Q}\otimes \operatorname{Hom}(X,B) \rightarrow \mathbf {Q}\otimes \operatorname{Hom}(X,C)\rightarrow 0 \] is exact for all rank-1 torsion-free abelian groups $X$. This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced sequences. As an application of our results concerning quasi-balanced sequences, the relationship between the two chains in the quasi-category of torsion-free abelian groups is illuminated.
LA - eng
KW - quasi-balanced; almost balanced; Kravchenko classes; quasi-balanced subgroups; almost balanced subgroups; Kravchenko classes; almost completely decomposable groups; torsion-free Abelian groups of finite rank; almost balanced exact sequences
UR - http://eudml.org/doc/248239
ER -

References

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Butler M.C.R., A class of torsion-free abelian groups of finite rank, Proc. London Math. Soc. 15 (1965), 680-698. (1965) Zbl0131.02501 MR0218446
Fuchs L., Infinite Abelian Groups, II Academic Press New York (1973). (1973) Zbl0257.20035 MR0349869
Kravchenko A.A., Balanced and cobalanced Butler groups, Math. Notes Acad. Sci. USSR 45 (1989), 369-373. (1989) Zbl0695.20032 MR1005459
Nongxa L.G., Vinsonhaler C., Balanced Butler groups, J. Algebra, to appear. Zbl0846.20060 MR1378545
Nongxa L.G., Vinsonhaler C., Balanced representations of partially ordered sets, to appear.
C. Vinsonhaler, A survey of balanced Butler groups and representations, Abelian Groups and Modules Lecture Notes in Pure and Applied Math. 182 Marcel Dekker (1996), 113-122. (1996) Zbl0865.20040 MR1415625

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