Butler groups of arbitrary cardinality |
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| Authors: | Laszlo Fuchs Menachem Magidor |
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| Affiliation: | (1) Department of Mathematics, Tulane University, 70118 New Orleans, LA, USA;(2) Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel;(3) Department of Mathematics, Massachusetts Institute of Technology, 02139 Cambridge, MA, USA |
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| 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 groupG and torsion groupT. Furthermore, balanced subgroups of completely decomposable groups are Butler groups. These results have been known, under CH, only for groups of cardinalities ≤ ℵω. Partial support by NSF is gratefully acknowledged. Partially supported by U.S.-Israel Binational Science Foundation. |
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