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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 71, Pages 4511-4516
http://dx.doi.org/10.1155/S016117120321067X

Characterization of the automorphisms having the lifting property in the category of abelian p-groups

Department of Mathematics and Computer Science, Faculty of Sciences, Mohammed V University, B.P.1014, Rabat, Morocco

Received 23 October 2002

Copyright © 2003 Hindawi Publishing Corporation. 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.

Abstract

Let p be a prime. It is shown that an automorphism α of an abelian p-group A lifts to any abelian p-group of which A is a homomorphic image if and only if α=πidA, with π an invertible p-adic integer. It is also shown that if A is torsion group or torsion-free p-divisible group, then idA and idA are the only automorphisms of A which possess the lifting property in the category of abelian groups.