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.
@article{bwmeta1.element.doi-10_2478_s11533-006-0040-7,
author = {Maria Nogin},
title = {A short proof of Eilenberg and Moore's theorem},
journal = {Open Mathematics},
volume = {5},
year = {2007},
pages = {201-204},
zbl = {1120.20054},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0040-7}
}
Maria Nogin. A short proof of Eilenberg and Moore’s theorem. Open Mathematics, Tome 5 (2007) pp. 201-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0040-7/
[1] S. Eilenberg and J.C. Moore: “Foundations of relative homological algebra”, Mem. Amer. Math. Soc., Vol. 55, (1965). | Zbl 0129.01101
[2] G. Higman, B. Newmann and H. Newmann: “Embedding theorem for groups”, J. London Math. Soc., Vol. 24, (1949). | Zbl 0112.26001
[3] 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.