Geodesic
Quasi-P-Pure-Injective Groups
Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 578-586

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Benabdallah, Khalid; Laroche, Adele. Quasi-P-Pure-Injective Groups. Canadian journal of mathematics, Tome 29 (1977) no. 3, pp. 578-586. doi: 10.4153/CJM-1977-059-5
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[1] 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] 2. Benabdallah, K. et Laroche, A., Sur le problème 17 de L. Fuchs, Ann. Se. Math. Quebec 1 (1977), 63–65. Google Scholar

[3] 3. Benabdallah, K. et Laroche, A., Sur les groupes quasi-pur s-infectifs ‘sans torsion, to appear, Rendiconti di Mathematica, Italy. Google Scholar

[4] 4. Bourbaki, N., Algèbre, ch. VII (Hermann, Paris, 1952). Google Scholar

[5] 5. Fuchs, L., Infinite abelian groups, vol. I (Academic Press, New York, 1970). Google Scholar

[6] 6. Fuchs, L. Infinite abelian groups, vol. II (Academic Press, New York, 1973). Google Scholar

[7] 7. Griffith, P., Infinite abelian groups, Chicago Lectures in Mathematics, Chicago and London, 1970. Google Scholar

[8] 8. Mader, A., The fully invariant subgroups of reduced algebraically compact groups, Publ. Math. Debrecen, A. (1970), 299–306. Google Scholar

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