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Finite quasi-injective groups

Published online by Cambridge University Press:  18 May 2009

Dennis Bertholf  and
Gary Walls
Dennis Bertholf
Affiliation:
Mathematics Department, Oklahoma State University, Stillwater, Oklahoma 74074
Gary Walls
Affiliation:
Southern Station, Box 9265, University of Southern Mississippi, Hattiesburg, Mississippi 39401
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 20 , Issue 1 , January 1979 , pp. 29 - 33
Copyright
Copyright © Glasgow Mathematical Journal Trust 1979

References

REFERENCES

1.Bertholf, D. and Walls, G. L., Slightly injective finite groups, unpublished.Google Scholar
2.Fuchs, L., Infinite abelian groups I (Academic Press, 1970).Google Scholar
3.Gorenstein, D., Finite groups (Harper and Row, 1968).Google Scholar
4.Huppert, B., Endliche Gruppen I (Springer, 1967).Google Scholar
5.Scott, W. R., Group theory (Prentice-Hall, 1964).Google Scholar