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Quasi-P-Pure-Injective Groups

Published online by Cambridge University Press:  20 November 2018

Khalid Benabdallah  and
Adele Laroche
Khalid Benabdallah
Affiliation:
Université de Montréal, Montréal, Québec
Adele Laroche
Affiliation:
Université de Montréal, Montréal, Québec
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Abstract

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Recently, a great deal of attention has been paid to the concept of quasipure injectivity introduced by L. Fuchs as Problem 17 in [5]. An abelian group G is said to be quasi-pure-injective (q.p.i.) if every homomorphism from a pure subgroup of G to G can be lifted to an endomorphism of G. D. M. Arnold, B. O'Brien and J. D. Reid have succeeded in [1] to characterize torsion free q.p.i. of finite rank, whereas in [2] we solved the torsion case and in [3] we studied certain classes of infinite rank torsion free q.p.i. groups.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 578 - 586
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Arnold, D. M., O'Brien, B. and Reid, J. D., Torsion-free abelian q.p.i. and q.p.p. groups* Preliminary report, Notices of the American Mathematical Society, January 1976.Google Scholar
2. Benabdallah, K. et Laroche, A., Sur le problème 17 de L. Fuchs, Ann. Se. Math. Quebec 1 (1977), 63–65.Google Scholar
3. Benabdallah, K. et Laroche, A., Sur les groupes quasi-pur s-infectifs ‘sans torsion, to appear, Rendiconti di Mathematica, Italy.Google Scholar
4. Bourbaki, N., Algèbre, ch. VII (Hermann, Paris, 1952).Google Scholar
5. Fuchs, L., Infinite abelian groups, vol. I (Academic Press, New York, 1970).Google Scholar
6. Fuchs, L. Infinite abelian groups, vol. II (Academic Press, New York, 1973).Google Scholar
7. Griffith, P., Infinite abelian groups, Chicago Lectures in Mathematics, Chicago and London, 1970.Google Scholar
8. Mader, A., The fully invariant subgroups of reduced algebraically compact groups, Publ. Math. Debrecen, A. (1970), 299–306.Google Scholar