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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homology in varieties of groups. II


Author: C. R. Leedham-Green
Journal: Trans. Amer. Math. Soc. 162 (1971), 15-25
MSC: Primary 20.50; Secondary 18.00
Part I: Trans. Amer. Math. Soc. (1971), 1-14
Part III: Trans. Amer. Math. Soc. (1971), 27-33
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Abstract: The study of (co-) homology groups $ {\mathfrak{B}_n}(\Pi ,A)$, $ {\mathfrak{B}^n}(\Pi ,A),\mathfrak{B}$ a variety, II a group in $ \mathfrak{B}$, and A a suitable II-module, is pursued. They are compared with a certain Tor and Ext. The definition of the homology of an epimorphism due to Rinehart is shown to agree with that due to Barr and Beck (whenever both are defined). The edge effects of a spectral sequence are calculated.


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DOI: http://dx.doi.org/10.1090/S0002-9947-71-99968-5
PII: S 0002-9947(71)99968-5
Keywords: Homology in varieties of groups, universal coefficients, spectral sequence, Rinehart's exact sequence
Article copyright: © Copyright 1971 American Mathematical Society