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A note on group extensions

Published online by Cambridge University Press:  09 April 2009

L. R. Vermani
L. R. Vermani
Affiliation:
Department of MathematicsUniversity of Exeter, Exeter, England
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In [2] Hauptfleisch proved that if A, B, H, K are Abelian groups, φ:A → H and ψ:B → K are epimorphisms, then every central group extension G of H by K is homomorphic image of a central loop extension L of A by B. The aim of the present note is to prove (using almost the same argument as in [2])

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 4 , December 1974 , pp. 509 - 510
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Eilenberg, S. and MacLane, S., ‘Algebraic cohomology groups and loops’, Duke Math. J. 14 (1947), 435–463.Google Scholar
[2]Hauptfleisch, G. J., ‘A note on central group extensions’, J. Austral. Math. Soc. 15 (1973), 428–429.CrossRefGoogle Scholar