In this paper we give a short and simple proof the following theorem of S. Eilenberg and J.C. Moore: the only injective object in the category of groups is the trivial group.
 S. Eilenberg and J.C. Moore: “Foundations of relative homological algebra”, Mem. Amer. Math. Soc., Vol. 55, (1965). Search in Google Scholar
 G. Higman, B. Newmann and H. Newmann: “Embedding theorem for groups”, J. London Math. Soc., Vol. 24, (1949). Search in Google Scholar
 M.S. Voloshina (Nogin): On the holomorph of the discrete group, Thesis (Ph.D.), University of Rochester, 2003, http://arxiv.org/pdf/math.GR/0302120. Search in Google Scholar
© 2007 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.