| Title:
|
The nonseparability of simply presented mixed groups (English) |
| Author:
|
Hill, Paul |
| Author:
|
Megibben, Charles |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
1-5 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is demonstrated that an isotype subgroup of a simply presented abelian group can be simply presented without being a separable subgroup. In particular, the conjecture based on a variety of special cases that Warfield groups are absolutely separable is disproved. (English) |
| Keyword:
|
Warfield groups |
| Keyword:
|
simply presented |
| Keyword:
|
isotype subgroup |
| Keyword:
|
separable subgroup |
| MSC:
|
20F05 |
| MSC:
|
20K21 |
| MSC:
|
20K27 |
| idZBL:
|
Zbl 0943.20053 |
| idMR:
|
MR1622308 |
| . |
| Date available:
|
2009-01-08T18:38:27Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118979 |
| . |
| Reference:
|
[AH] Albrecht U., Hill P.: Butler groups of infinite rank and axiom 3.Czechoslovak Math. Jour. 37 (1987), 293-309. Zbl 0628.20045, MR 0882600 |
| Reference:
|
[B] Baer R.: Abelian groups without elements of finite order.Duke Math. Jour. 3 (1937), 68-122. Zbl 0016.20303, MR 1545974 |
| Reference:
|
[DR] Dugas M., Rangaswamy K.M.: Separable pure subgroups of completely decomposable torsion-free groups.Arch. Math. (Basel) (1992), 332-337. MR 1152619 |
| Reference:
|
[F] Fuchs L.: Infinite Abelian Groups.II Academic Press New York (1973). Zbl 0257.20035, MR 0349869 |
| Reference:
|
[H1] Hill P.: On the classification of abelian groups.photocopied manuscript, 1967. |
| Reference:
|
[H2] Hill P.: Isotype subgroups of totally projective groups.Lecture Notes in Math. 874 Springer-Verlag New York (1973), 305-321. MR 0645937 |
| Reference:
|
[HM1] Hill P., Megibben C.: On the theory and classification of abelian p-groups.Math. Zeit. 190 (1985), 17-38. Zbl 0535.20031, MR 0793345 |
| Reference:
|
[HM2] Hill P., Megibben C.: Axiom 3 modules.Trans. Amer. Math. Soc. 295 (1986), 715-734. Zbl 0597.20048, MR 0833705 |
| Reference:
|
[HM3] Hill P., Megibben C.: Pure subgroups of torsion-free groups.Trans. Amer. Math. Soc. 303 (1987), 765-778. Zbl 0627.20028, MR 0902797 |
| Reference:
|
[HM4] Hill P., Megibben C.: Knice subgroups of mixed groups.Abelian Group Theory Gordon-Breach New York (1987), 765-778. Zbl 0653.20057, MR 1011306 |
| Reference:
|
[HR] Hunter R., Richman F.: Global Warfield groups.Trans. Amer. Math. Soc. 266 (1981), 555-572. Zbl 0471.20038, MR 0617551 |
| Reference:
|
[Wal] Wallace K.: On mixed groups of torsion-free rank one with totally projective primary components.Jour. Algebra 17 (1971), 482-488. Zbl 0215.39902, MR 0272891 |
| Reference:
|
[War] Warfield R.: A classification theorem for abelian p-groups.Trans. Amer. Math. Soc. 210 (1975), 149-168. Zbl 0324.20058, MR 0372071 |
| . |
