Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
Warfield groups; simply presented; isotype subgroup; separable subgroup
Warfield groups; simply presented; isotype subgroup; separable subgroup
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.
References:
[AH] Albrecht U., Hill P.: Butler groups of infinite rank and axiom 3. Czechoslovak Math. Jour. 37 (1987), 293-309. MR 0882600 | Zbl 0628.20045
[B] Baer R.: Abelian groups without elements of finite order. Duke Math. Jour. 3 (1937), 68-122. MR 1545974 | Zbl 0016.20303
[DR] Dugas M., Rangaswamy K.M.: Separable pure subgroups of completely decomposable torsion-free groups. Arch. Math. (Basel) (1992), 332-337. MR 1152619
[F] Fuchs L.: Infinite Abelian Groups. II Academic Press New York (1973). MR 0349869 | Zbl 0257.20035
[H1] Hill P.: On the classification of abelian groups. photocopied manuscript, 1967.
[H2] Hill P.: Isotype subgroups of totally projective groups. Lecture Notes in Math. 874 Springer-Verlag New York (1973), 305-321. MR 0645937
[HM1] Hill P., Megibben C.: On the theory and classification of abelian p-groups. Math. Zeit. 190 (1985), 17-38. MR 0793345 | Zbl 0535.20031
[HM2] Hill P., Megibben C.: Axiom 3 modules. Trans. Amer. Math. Soc. 295 (1986), 715-734. MR 0833705 | Zbl 0597.20048
[HM3] Hill P., Megibben C.: Pure subgroups of torsion-free groups. Trans. Amer. Math. Soc. 303 (1987), 765-778. MR 0902797 | Zbl 0627.20028
[HM4] Hill P., Megibben C.: Knice subgroups of mixed groups. Abelian Group Theory Gordon-Breach New York (1987), 765-778. MR 1011306 | Zbl 0653.20057
[HR] Hunter R., Richman F.: Global Warfield groups. Trans. Amer. Math. Soc. 266 (1981), 555-572. MR 0617551 | Zbl 0471.20038
[Wal] Wallace K.: On mixed groups of torsion-free rank one with totally projective primary components. Jour. Algebra 17 (1971), 482-488. MR 0272891 | Zbl 0215.39902
[War] Warfield R.: A classification theorem for abelian p-groups. Trans. Amer. Math. Soc. 210 (1975), 149-168. MR 0372071 | Zbl 0324.20058
Search
Partner of
