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.
@article{118979, author = {Paul Hill and Charles K. Megibben}, title = {The nonseparability of simply presented mixed groups}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {39}, year = {1998}, pages = {1-5}, zbl = {0943.20053}, mrnumber = {1622308}, language = {en}, url = {http://dml.mathdoc.fr/item/118979} }
Hill, Paul; Megibben, Charles K. The nonseparability of simply presented mixed groups. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 1-5. http://gdmltest.u-ga.fr/item/118979/
Butler groups of infinite rank and axiom 3, Czechoslovak Math. Jour. 37 (1987), 293-309. (1987) | MR 0882600 | Zbl 0628.20045
Abelian groups without elements of finite order, Duke Math. Jour. 3 (1937), 68-122. (1937) | MR 1545974 | Zbl 0016.20303
Separable pure subgroups of completely decomposable torsion-free groups, Arch. Math. (Basel) (1992), 332-337. (1992) | MR 1152619
Infinite Abelian Groups, II Academic Press New York (1973). (1973) | MR 0349869 | Zbl 0257.20035
On the classification of abelian groups, photocopied manuscript, 1967.
Isotype subgroups of totally projective groups, Lecture Notes in Math. 874 Springer-Verlag New York (1973), 305-321. (1973) | MR 0645937
On the theory and classification of abelian p-groups, Math. Zeit. 190 (1985), 17-38. (1985) | MR 0793345 | Zbl 0535.20031
Axiom 3 modules, Trans. Amer. Math. Soc. 295 (1986), 715-734. (1986) | MR 0833705 | Zbl 0597.20048
Pure subgroups of torsion-free groups, Trans. Amer. Math. Soc. 303 (1987), 765-778. (1987) | MR 0902797 | Zbl 0627.20028
Knice subgroups of mixed groups, Abelian Group Theory Gordon-Breach New York (1987), 765-778. (1987) | MR 1011306 | Zbl 0653.20057
Global Warfield groups, Trans. Amer. Math. Soc. 266 (1981), 555-572. (1981) | MR 0617551 | Zbl 0471.20038
On mixed groups of torsion-free rank one with totally projective primary components, Jour. Algebra 17 (1971), 482-488. (1971) | MR 0272891 | Zbl 0215.39902
A classification theorem for abelian p-groups, Trans. Amer. Math. Soc. 210 (1975), 149-168. (1975) | MR 0372071 | Zbl 0324.20058