International Journal of Mathematics and Mathematical Sciences 
Volume 3 (1980), Issue 4, Pages 719-730
doi:10.1155/S016117128000052X

Extensions of group retractions

Richard D. Byrd, Justin T. Lloyd, Roberto A. Mena, and J. Roger Teller

 Department of Mathematics, University of Houston, Houston 77004, Texas, USA
Received 18 June 1979; Revised 29 February 1980

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.