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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 1, 2007

A short proof of Eilenberg and Moore’s theorem

  • Maria Nogin EMAIL logo
From the journal Open Mathematics


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.

MSC: 20J15; 14H30

[1] S. Eilenberg and J.C. Moore: “Foundations of relative homological algebra”, Mem. Amer. Math. Soc., Vol. 55, (1965). Search in Google Scholar

[2] G. Higman, B. Newmann and H. Newmann: “Embedding theorem for groups”, J. London Math. Soc., Vol. 24, (1949). Search in Google Scholar

[3] M.S. Voloshina (Nogin): On the holomorph of the discrete group, Thesis (Ph.D.), University of Rochester, 2003, Search in Google Scholar

Published Online: 2007-3-1
Published in Print: 2007-3-1

© 2007 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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