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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Crossed extensions


Author: John G. Ratcliffe
Journal: Trans. Amer. Math. Soc. 257 (1980), 73-89
MSC: Primary 20J10; Secondary 18G15
MathSciNet review: 549155
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Abstract: We develop a natural five term exact sequence relating the second and third cohomology of groups. We show that this sequence is the proper framework for the problem of realizing an abstract kernel. As an application, we give an interpretation of the third cohomology of a group in terms of crossed sequences.


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DOI: https://doi.org/10.1090/S0002-9947-1980-0549155-0
Keywords: Abstract kernels, cohomology of groups, crossed modules, cup products, Mac Lane-Whitehead obstruction
Article copyright: © Copyright 1980 American Mathematical Society