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: 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.

**[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)**

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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