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International Journal of Mathematics and Mathematical Sciences
Volume 3, Issue 4, Pages 719-730
http://dx.doi.org/10.1155/S016117128000052X

Extensions of group retractions

Department of Mathematics, University of Houston, Houston 77004, Texas, USA

Received 18 June 1979; Revised 29 February 1980

Copyright © 1980 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

In this paper a condition, which is necessary and sufficient, is determined when a retraction of a subgroup H of a torsion-free group G can be extended to a retraction of G. It is also shown that each retraction of a torsion-free abelian group can be uniquely extended to a retraction of its divisible closure.