Abstract
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.
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References
S. Eilenberg and J.C. Moore: “Foundations of relative homological algebra”, Mem. Amer. Math. Soc., Vol. 55, (1965).
G. Higman, B. Newmann and H. Newmann: “Embedding theorem for groups”, J. London Math. Soc., Vol. 24, (1949).
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.
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This work first appeared as a part of the author’s Ph.D. dissertation [3]
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Nogin, M. A short proof of Eilenberg and Moore’s theorem. centr.eur.j.math. 5, 201–204 (2007). https://doi.org/10.2478/s11533-006-0040-7
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DOI: https://doi.org/10.2478/s11533-006-0040-7