# A short proof of Eilenberg and Moore’s theorem

Open Mathematics (2007)

- Volume: 5, Issue: 1, page 201-204
- ISSN: 2391-5455

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topMaria Nogin. "A short proof of Eilenberg and Moore’s theorem." Open Mathematics 5.1 (2007): 201-204. <http://eudml.org/doc/269468>.

@article{MariaNogin2007,

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.},

author = {Maria Nogin},

journal = {Open Mathematics},

keywords = {Group; injective; fundamental group; covering space; categories of groups; injective groups; fundamental groups; covering spaces},

language = {eng},

number = {1},

pages = {201-204},

title = {A short proof of Eilenberg and Moore’s theorem},

url = {http://eudml.org/doc/269468},

volume = {5},

year = {2007},

}

TY - JOUR

AU - Maria Nogin

TI - A short proof of Eilenberg and Moore’s theorem

JO - Open Mathematics

PY - 2007

VL - 5

IS - 1

SP - 201

EP - 204

AB - 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.

LA - eng

KW - Group; injective; fundamental group; covering space; categories of groups; injective groups; fundamental groups; covering spaces

UR - http://eudml.org/doc/269468

ER -

## References

top- [1] S. Eilenberg and J.C. Moore: “Foundations of relative homological algebra”, Mem. Amer. Math. Soc., Vol. 55, (1965). Zbl0129.01101
- [2] G. Higman, B. Newmann and H. Newmann: “Embedding theorem for groups”, J. London Math. Soc., Vol. 24, (1949). Zbl0112.26001
- [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.

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