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
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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.
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- [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)
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- [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)
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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