Butler groups and Shelah's Singular Compactness
Bican, Ladislav
Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996), p. 171-178 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

A torsion-free group is a $B_2$-group if and only if it has an axiom-3 family $\frak C$ of decent subgroups such that each member of $\frak C$ has such a family, too. Such a family is called $SL_{\aleph_0}$-family. Further, a version of Shelah's Singular Compactness having a rather simple proof is presented. As a consequence, a short proof of a result [R1] stating that a torsion-free group $B$ in a prebalanced and TEP exact sequence $0 \to K \to C \to B \to 0$ is a $B_2$-group provided $K$ and $C$ are so.

Publié le : 1996-01-01
Classification:  20K20,  20K27 
@article{118821,
     author = {Ladislav Bican},
     title = {Butler groups and Shelah's Singular Compactness},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {37},
     year = {1996},
     pages = {171-178},
     zbl = {0857.20037},
     mrnumber = {1396169},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118821}
}

Bican, Ladislav. Butler groups and Shelah's Singular Compactness. Commentationes Mathematicae Universitatis Carolinae, Tome 37 (1996) pp. 171-178. http://gdmltest.u-ga.fr/item/118821/

Albrecht U.; Hill P. Butler groups of infinite rank and axiom 3, Czech. Math. J. 37 (1987), 293-309. (1987) | MR 0882600 | Zbl 0628.20045

Bican L. Purely finitely generated groups, Comment. Math. Univ. Carolinae 21 (1980), 209-218. (1980) | MR 0580678

Bican L. Butler groups of infinite rank, Czech. Math. J. 44 (119) (1994), 67-79. (1994) | MR 1257937 | Zbl 0812.20032

Bican L. On $B_2$-groups, Contemporary Math. 171 (1994), 13-19. (1994) | MR 1293129

Bican L. Families of preseparative subgroups, to appear. | MR 1415629 | Zbl 0866.20043

Bican L.; Fuchs L. Subgroups of Butler groups, Communications in Algebra 22 (1994), 1037-1047. (1994) | MR 1261020 | Zbl 0802.20045

Bican L.; Salce L. Infinite rank Butler groups, Proc. Abelian Group Theory Conference, Honolulu Lecture Notes in Math., Springer-Verlag 1006 (1983), 171-189. (1983)

Butler M.C.R. A class of torsion-free abelian groups of finite rank, Proc. London Math. Soc. 15 (1965), 680-698. (1965) | MR 0218446 | Zbl 0131.02501

Dugas M.; Hill P.; Rangaswamy K.M. Infinite rank Butler groups II, Trans. Amer. Math. Soc. 320 (1990), 643-664. (1990) | MR 0963246

Fuchs L. Infinite Abelian Groups, vol. I and II, Academic Press New York (1973 and 1977). (1973 and 1977) | MR 0255673

Fuchs L. Infinite rank Butler groups, preprint.

Hodges W. In singular cardinality, locally free algebras are free, Algebra Universalis 12 (1981), 205-220. (1981) | MR 0608664 | Zbl 0476.03039

Rangaswamy K.M. A homological characterization of abelian $B_2$-groups, Comment. Math. Univ. Carolinae 35 (1994), 627-631. (1994)

Rangaswamy K.M. A property of $B_2$-groups, Proc. Amer. Math. Soc. 121 (1994), 409-415. (1994) | MR 1186993