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논문검색

Information Center for Mathematical Science

논문검색

Journal of Pure and Applied Algebra
( Vol. 98 NO.1 / (1995))
Butler Groups of Infinite Rank
L. Fuchs,
Pages. 25-44
Abstract Butler groups are torsion-free abelian groups which -in the infinite rank case - can be defined in two different ways. One definition requires that all the balanced extensions of torsion groups by term are splitting, while the other stipulates that they admit continuous transfinite chains (with finite rank factors) of so-called decent subgroups.\
This paper is devoted to the three major questions for Butler groups of finite rank: Are the two definitions equivalent? Are balanced subgroups of completely decomposable torsion-free groups always Butler groups? Which pure subgroups of Butler groups are again Butler groups? In attacking these problems, a new approach is used by utilizing $aleph_0$-prebalanced chains and relative balanced-projective resolutions introduced by Bican Fuchs [5].\
A noteworthy feature is that no additional set-theoretical hypotheses are
needed.
Contents 0. Introduction
1. Preliminaries
2. $\kappa$-prebalanced chains
3. Axiom-3 families of $\aleph_0$-prebalanced subgroups
4. $B_1$-groups with $\aleph_0$-prebalanced chains
5. A homological characterization of $B_2$-group
6. Groups without $\aleph_i$-prebalanced chains
7. The groups Bext$^n$
8. Subgroups of $B_2$-groups
Key words
Mathmatical Subject Classification