International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 71, Pages 4511-4516
Characterization of the automorphisms having the lifting property in the category of abelian -groups
Department of Mathematics and Computer Science, Faculty of Sciences, Mohammed V University, B.P.1014, Rabat, Morocco
Received 23 October 2002
Copyright © 2003 S. Abdelalim and H. Essannouni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a prime. It is shown that an automorphism of an abelian -group lifts to any abelian -group of which is a homomorphic image if and only if , with an invertible -adic integer. It is also shown that if is torsion group or torsion-free -divisible group, then and are the only automorphisms of which possess the lifting property in the category of abelian groups.