Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Quasi-pure projective and injective torsion groups


Authors: W. P. Berlinghoff and J. D. Reid
Journal: Proc. Amer. Math. Soc. 65 (1977), 189-193
MSC: Primary 20K10
DOI: https://doi.org/10.1090/S0002-9939-1977-0470104-3
MathSciNet review: 0470104
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper characterizes quasi-pure projective (q.p.p.) and quasi-pure injective (q.p.i.) p-groups, and hence characterizes all such (abelian) torsion groups. A p-group is q.p.i. if and only if it is the direct sum of a divisible group and a torsion complete group. A nonreduced p-group is q.p.p. if and only if it is the direct sum of a divisible group and a bounded group; a reduced p-group is q.p.p. if and only if it is a direct sum of cyclic groups.


References [Enhancements On Off] (What's this?)

  • [1] D. Arnold, B. O'Brien and J. D. Reid, Torsion free abelian q.p.i. and q.p.p. groups (to appear).
  • [2] D. Arnold, C. I. Vinsonhaler and W. J. Wickless, Quasi-pure projective and injective torsion free abelian groups of rank 2, Rocky Mountain J. Math. 6 (1976), 61-70. MR 0444799 (56:3146)
  • [3] K. Benabdallah and R. Bradley, oral communication.
  • [4] L. Fuchs, Infinite abelian groups, Vols. I, II, Academic Press, New York, 1970. MR 0255673 (41:333)
  • [5] Paul Hill, The covering theorem for upper basic subgroups, Michigan Math. J. 18 (1971), 187-192. MR 0281798 (43:7512)
  • [6] J. D. Reid, C. I. Vinsonhaler and W. J. Wickless, Quasi-pure projectivity and two generalizations (to appear).
  • [7] Dalton Tarwater and Elbert Walker, Decompositions of direct sums of cyclic p-groups, Rocky Mountain J. Math. 2 (1972), 275-282. MR 0299685 (45:8733)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20K10

Retrieve articles in all journals with MSC: 20K10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0470104-3
Keywords: Abelian group, pure exact sequence, quasi-projective, quasi-injective, torsion complete, direct sum of cyclic groups
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society