Butler groups of arbitrary cardinality

Laszlo Fuchs; Menachem Magidor

doi:10.1007/BF02761702

Butler groups of arbitrary cardinality

Laszlo Fuchs^*
, Menachem Magidor

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We show that in the constructible universe, the two usual definitions of Butler groups are equivalent for groups of arbitrarily large power. We also prove that Bext²(G, T) vanishes for every torsion-free group G and torsion group T. Furthermore, balanced subgroups of completely decomposable groups are Butler groups. These results have been known, under CH, only for groups of cardinalities ≤ א_ω.

Original language	English
Pages (from-to)	239-263
Number of pages	25
Journal	Israel Journal of Mathematics
Volume	84
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02761702
State	Published - Feb 1993

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10.1007/BF02761702

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AB - We show that in the constructible universe, the two usual definitions of Butler groups are equivalent for groups of arbitrarily large power. We also prove that Bext2(G, T) vanishes for every torsion-free group G and torsion group T. Furthermore, balanced subgroups of completely decomposable groups are Butler groups. These results have been known, under CH, only for groups of cardinalities ≤ אω.

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Butler groups of arbitrary cardinality

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