Geodesic
Almost Butler groups
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 367-378

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR   Zbl

Generalizing the notion of the almost free group we introduce almost Butler groups. An almost $B_2$-group $G$ of singular cardinality is a $B_2$-group. Since almost $B_2$-groups have preseparative chains, the same result in regular cardinality holds under the additional hypothesis that $G$ is a $B_1$-group. Some other results characterizing $B_2$-groups within the classes of almost $B_1$-groups and almost $B_2$-groups are obtained. A theorem of stating that a group $G$ of weakly compact cardinality $\lambda $ having a $\lambda $-filtration consisting of pure $B_2$-subgroup is a $B_2$-group appears as a corollary.
Generalizing the notion of the almost free group we introduce almost Butler groups. An almost $B_2$-group $G$ of singular cardinality is a $B_2$-group. Since almost $B_2$-groups have preseparative chains, the same result in regular cardinality holds under the additional hypothesis that $G$ is a $B_1$-group. Some other results characterizing $B_2$-groups within the classes of almost $B_1$-groups and almost $B_2$-groups are obtained. A theorem of stating that a group $G$ of weakly compact cardinality $\lambda $ having a $\lambda $-filtration consisting of pure $B_2$-subgroup is a $B_2$-group appears as a corollary.
Classification : 20K20, 20K27 
Bican, Ladislav. Almost Butler groups. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 367-378. http://geodesic.mathdoc.fr/item/CMJ_2000_50_2_a11/
@article{CMJ_2000_50_2_a11,
     author = {Bican, Ladislav},
     title = {Almost {Butler} groups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {367--378},
     year = {2000},
     volume = {50},
     number = {2},
     mrnumber = {1761394},
     zbl = {1051.20023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2000_50_2_a11/}
}
TY  - JOUR
AU  - Bican, Ladislav
TI  - Almost Butler groups
JO  - Czechoslovak Mathematical Journal
PY  - 2000
SP  - 367
EP  - 378
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2000_50_2_a11/
LA  - en
ID  - CMJ_2000_50_2_a11
ER  - 
%0 Journal Article
%A Bican, Ladislav
%T Almost Butler groups
%J Czechoslovak Mathematical Journal
%D 2000
%P 367-378
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2000_50_2_a11/
%G en
%F CMJ_2000_50_2_a11

[AH] Albrecht, U., Hill, P.: Butler groups of infinite rank and axiom 3. Czechoslovak Math. J. 37 (1987), 293–309. | MR

[B1] Bican, L.: On $B_2$-groups. Contemp. Math. 171 (1994), 13–19. | MR

[B2] Bican, L.: Butler groups and Shelah’s singular compactness. Comment. Math. Univ. Carolin. 37 (1996), 11–178. | MR | Zbl

[B3] Bican, L.: Families of preseparative subgroups. Abelian groups and modules, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Inc. 182 (1996), 149–162. | MR | Zbl

[BB] El Bashir, R., Bican, L.: Remarks on $B_2$-groups. Abelian groups and modules, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Inc. 182 (1996), 133–142.

[BF] Bican, L., Fuchs, L.: Subgroups of Butler groups. Comm. Algebra 22 (1994), 1037–1047. | DOI | MR

[BR] Bican, L., Rangaswamy, K. M.: Smooth unions of Butler groups. Forum Math. 10 (1998), 233–247. | DOI | MR

[BRV] Bican, L., Rangaswamy, K. M., Vinsonhaler Ch.: Butler groups as smooth ascending unions. (to appear). | MR

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

[DHR] Dugas, M., Hill, P., Rangaswamy, K. M.: Infinite rank Butler groups II. Trans. Amer. Math. Soc. 320 (1990), 643–664. | MR

[DR] Dugas, Rangaswamy, K. M.: Infinite rank Butler groups. Trans. Amer. Math. Soc. 305 (1988), 129–142. | DOI | MR

[F1] Fuchs, L.: Infinite Abelian Groups, vol. I and II. Academic Press, New York, 1973 and 1977. | MR

[F2] Fuchs, L.: Infinite rank Butler groups. Preprint.

[F3] Fuchs, L.: Infinite rank Butler groups. J. Pure Appl. Algebra 98 (1995), 25–44. | DOI | MR

[FMa] Fuchs, L., Magidor, M.: Butler groups of arbitrary cardinality. Israel J. Math. 84 (1993), 239–263. | DOI | MR

[FR1] Fuchs, L., Rangaswamy, K. M.: Butler groups that are unions of subgroups with countable typesets. Arch. Math. 61 (1993), 105–110. | DOI | MR

[FR2] Fuchs, L., Rangaswamy, K. M.: Unions of chains of Butler groups. Contemp. Math. 171 (1994), 141–146. | DOI | MR

[FV] Fuchs, L., Viljoen, G.: Note on the extensions of Butler groups. Bull. Austral. Math. Soc. 41 (1990), 117–122. | DOI | MR

[H] Hodges, W.: In singular cardinality, locally free algebras are free. Algebra Universalis 12 (1981), 205–220. | DOI | MR | Zbl

[R] Rangaswamy, K. M.: A property of $B_2$-groups. Comment. Math. Univ. Carolin. 35 (1994), 627–631. | MR