The nonseparability of simply presented mixed groups

Paul Hill; Charles K. Megibben

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 1, page 1-5
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Hill, Paul, and Megibben, Charles K.. "The nonseparability of simply presented mixed groups." Commentationes Mathematicae Universitatis Carolinae 39.1 (1998): 1-5. <http://eudml.org/doc/248261>.

@article{Hill1998,
abstract = {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.},
author = {Hill, Paul, Megibben, Charles K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Warfield groups; simply presented; isotype subgroup; separable subgroup; Warfield groups; simply presented Abelian groups; isotype subgroups; separable subgroups},
language = {eng},
number = {1},
pages = {1-5},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The nonseparability of simply presented mixed groups},
url = {http://eudml.org/doc/248261},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Hill, Paul
AU - Megibben, Charles K.
TI - The nonseparability of simply presented mixed groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 1
SP - 1
EP - 5
AB - 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.
LA - eng
KW - Warfield groups; simply presented; isotype subgroup; separable subgroup; Warfield groups; simply presented Abelian groups; isotype subgroups; separable subgroups
UR - http://eudml.org/doc/248261
ER -

References

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  1. Albrecht U., Hill P., Butler groups of infinite rank and axiom 3, Czechoslovak Math. Jour. 37 (1987), 293-309. (1987) Zbl0628.20045MR0882600
  2. Baer R., Abelian groups without elements of finite order, Duke Math. Jour. 3 (1937), 68-122. (1937) Zbl0016.20303MR1545974
  3. Dugas M., Rangaswamy K.M., Separable pure subgroups of completely decomposable torsion-free groups, Arch. Math. (Basel) (1992), 332-337. (1992) MR1152619
  4. Fuchs L., Infinite Abelian Groups, II Academic Press New York (1973). (1973) Zbl0257.20035MR0349869
  5. Hill P., On the classification of abelian groups, photocopied manuscript, 1967. 
  6. Hill P., Isotype subgroups of totally projective groups, Lecture Notes in Math. 874 Springer-Verlag New York (1973), 305-321. (1973) MR0645937
  7. Hill P., Megibben C., On the theory and classification of abelian p-groups, Math. Zeit. 190 (1985), 17-38. (1985) Zbl0535.20031MR0793345
  8. Hill P., Megibben C., Axiom 3 modules, Trans. Amer. Math. Soc. 295 (1986), 715-734. (1986) Zbl0597.20048MR0833705
  9. Hill P., Megibben C., Pure subgroups of torsion-free groups, Trans. Amer. Math. Soc. 303 (1987), 765-778. (1987) Zbl0627.20028MR0902797
  10. Hill P., Megibben C., Knice subgroups of mixed groups, Abelian Group Theory Gordon-Breach New York (1987), 765-778. (1987) Zbl0653.20057MR1011306
  11. Hunter R., Richman F., Global Warfield groups, Trans. Amer. Math. Soc. 266 (1981), 555-572. (1981) Zbl0471.20038MR0617551
  12. Wallace K., On mixed groups of torsion-free rank one with totally projective primary components, Jour. Algebra 17 (1971), 482-488. (1971) Zbl0215.39902MR0272891
  13. Warfield R., A classification theorem for abelian p-groups, Trans. Amer. Math. Soc. 210 (1975), 149-168. (1975) Zbl0324.20058MR0372071

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