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Extensions of Endomorphisms from the Higher Centres

Published online by Cambridge University Press:  20 November 2018

Franklin Haimo
Franklin Haimo*
Affiliation:
Washington University, St. Louis, Missouri
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If 0 → A → C → B → 0 is an exact sequence of abelian groups, if ƒ is a 2-cocyle for this extension, if α ∈ End A, and if β ∈ End B, then a necessary and sufficient condition that α extend to an endomorphism γ of C which induces β is that (M) αƒ and ƒβ be cohomologous ; see Montgomery (2). We shall extend this result to the case where 1 → A → G → B → 1 is an exact sequence of groups and A is abelian.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1250 - 1258
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Fuchs, L., Abelian groups (Budapest, 1958).Google Scholar
2.Ph. Montgomery, unpublished doctoral thesis, Washington University, St. Louis, 1964.Google Scholar