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The Functor Bext under the Negation of CH

The Functor Bext under the Negation of CH Abstract. We show that the negation of the continuum hypothesis implies that the derived functor Bext2 is not zero and there exist balanced subgroups of completely decomposable groups of rank ^i that are not Butler groups. 1980 Mathematics Subject Classification (1985 Revision): 20K20. § 0. Introduction All groups in this paper are abelian and our notations are Standard s in [Fu I/II]. A torsion-free group B of arbitrary rank is called a Butler group if Bext1 (B, ) = 0 for any torsion group T. Here Bext1^, T) denotes the subgroup of Ext (B, T) of all balanced exact extensions. We refer to [Ar] for an excellent survey on Butler groups of infinite rank and to [AH], [DHR] for more recent results. P. Hill introduced the notion of a separable subgroup A of a (torsion-free) group G. (This is not to be confused with the notion of a group G being "separable" in the sense of R. Baer). The subgroup A of G is separable if for any coset 4- A A there is a countable subset C of A such that for all a e A there is a c e C with | -h a \ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

The Functor Bext under the Negation of CH

Forum Mathematicum , Volume 3 (3) – Jan 1, 1991

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References (3)

Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1991.3.23
Publisher site
See Article on Publisher Site

Abstract

Abstract. We show that the negation of the continuum hypothesis implies that the derived functor Bext2 is not zero and there exist balanced subgroups of completely decomposable groups of rank ^i that are not Butler groups. 1980 Mathematics Subject Classification (1985 Revision): 20K20. § 0. Introduction All groups in this paper are abelian and our notations are Standard s in [Fu I/II]. A torsion-free group B of arbitrary rank is called a Butler group if Bext1 (B, ) = 0 for any torsion group T. Here Bext1^, T) denotes the subgroup of Ext (B, T) of all balanced exact extensions. We refer to [Ar] for an excellent survey on Butler groups of infinite rank and to [AH], [DHR] for more recent results. P. Hill introduced the notion of a separable subgroup A of a (torsion-free) group G. (This is not to be confused with the notion of a group G being "separable" in the sense of R. Baer). The subgroup A of G is separable if for any coset 4- A A there is a countable subset C of A such that for all a e A there is a c e C with | -h a \

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1991

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