A short proof of Eilenberg and Moore’s theorem
Open Mathematics (2007)
- Volume: 5, Issue: 1, page 201-204
- ISSN: 2391-5455
Access Full Article
top
Abstract
topHow to cite
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.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.