Almost Butler groups

Ladislav Bican

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 2, page 367-378
  • ISSN: 0011-4642

Abstract

top
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 λ having a λ -filtration consisting of pure B 2 -subgroup is a B 2 -group appears as a corollary.

How to cite

top

Bican, Ladislav. "Almost Butler groups." Czechoslovak Mathematical Journal 50.2 (2000): 367-378. <http://eudml.org/doc/30568>.

@article{Bican2000,
abstract = {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.},
author = {Bican, Ladislav},
journal = {Czechoslovak Mathematical Journal},
keywords = {-groups; -groups; almost Butler groups; descent subgroups; prebalanced subgroups},
language = {eng},
number = {2},
pages = {367-378},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Almost Butler groups},
url = {http://eudml.org/doc/30568},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Bican, Ladislav
TI - Almost Butler groups
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 367
EP - 378
AB - 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.
LA - eng
KW - -groups; -groups; almost Butler groups; descent subgroups; prebalanced subgroups
UR - http://eudml.org/doc/30568
ER -

References

top
  1. Butler groups of infinite rank and axiom 3, Czechoslovak Math. J. 37 (1987), 293–309. (1987) MR0882600
  2. On B 2 -groups, Contemp. Math. 171 (1994), 13–19. (1994) MR1293129
  3. Butler groups and Shelah’s singular compactness, Comment. Math. Univ. Carolin. 37 (1996), 11–178. (1996) Zbl0857.20037MR1396169
  4. Families of preseparative subgroups, Abelian groups and modules, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Inc. 182 (1996), 149–162. (1996) Zbl0866.20043MR1415629
  5. Remarks on B 2 -groups, Abelian groups and modules, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Inc. 182 (1996), 133–142. (1996) 
  6. 10.1080/00927879408824891, Comm. Algebra 22 (1994), 1037–1047. (1994) MR1261020DOI10.1080/00927879408824891
  7. 10.1515/form.10.2.233, Forum Math. 10 (1998), 233–247. (1998) MR1611959DOI10.1515/form.10.2.233
  8. Butler groups as smooth ascending unions, (to appear). (to appear) MR1785487
  9. Infinite rank Butler groups,, Proc. Abelian Group Theory Conference, Honolulu, Lecture Notes in Math., Springer-Verlag 1006 (1983), 171–189. (1983) 
  10. Infinite rank Butler groups II, Trans. Amer. Math. Soc. 320 (1990), 643–664. (1990) MR0963246
  11. 10.1090/S0002-9947-1988-0920150-X, Trans. Amer. Math. Soc. 305 (1988), 129–142. (1988) MR0920150DOI10.1090/S0002-9947-1988-0920150-X
  12. Infinite Abelian Groups, vol. I and II, Academic Press, New York, 1973 and 1977. (1973 and 1977) MR0255673
  13. Infinite rank Butler groups, Preprint. 
  14. 10.1016/0022-4049(94)00016-C, J. Pure Appl. Algebra 98 (1995), 25–44. (1995) MR1316995DOI10.1016/0022-4049(94)00016-C
  15. 10.1007/BF02761702, Israel J. Math. 84 (1993), 239–263. (1993) MR1244670DOI10.1007/BF02761702
  16. 10.1007/BF01207457, Arch. Math. 61 (1993), 105–110. (1993) MR1230938DOI10.1007/BF01207457
  17. 10.1090/conm/171/01769, Contemp. Math. 171 (1994), 141–146. (1994) MR1293138DOI10.1090/conm/171/01769
  18. 10.1017/S0004972700017901, Bull. Austral. Math. Soc. 41 (1990), 117–122. (1990) MR1043972DOI10.1017/S0004972700017901
  19. 10.1007/BF02483879, Algebra Universalis 12 (1981), 205–220. (1981) Zbl0476.03039MR0608664DOI10.1007/BF02483879
  20. A property of B 2 -groups, Comment. Math. Univ. Carolin. 35 (1994), 627–631. (1994) MR1321233

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.