Finite quasi-injective groups
Glasgow mathematical journal, Tome 20 (1979) no. 1, pp. 29-33
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It is well known that the category of finite groups has no non-trivial injective objects. In general, a group is said to be quasi-injective if for every subgroup H of G and homomorphism f:H → G there exists an endomorphism F:G → G such that F|H = G. In other words, a group is quasi-injective whenever each homomorphism from a subgroup into the group can be extended to the whole group.
Bertholf, Dennis; Walls, Gary. Finite quasi-injective groups. Glasgow mathematical journal, Tome 20 (1979) no. 1, pp. 29-33. doi: 10.1017/S0017089500003682
@article{10_1017_S0017089500003682,
author = {Bertholf, Dennis and Walls, Gary},
title = {Finite quasi-injective groups},
journal = {Glasgow mathematical journal},
pages = {29--33},
year = {1979},
volume = {20},
number = {1},
doi = {10.1017/S0017089500003682},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500003682/}
}
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