Homology in varieties of groups. II
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- by C. R. Leedham-Green PDF
- Trans. Amer. Math. Soc. 162 (1971), 15-25 Request permission
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.References
- C. R. Leedham-Green, Homology in varieties of groups. I, II, III, Trans. Amer. Math. Soc. 162 (1971), 1–14; ibid. 162 (1971), 15–25; 162 (1971), 27–33. MR 0284510, DOI 10.1090/S0002-9947-1971-0284510-2
- Saunders MacLane, Homology, 1st ed., Die Grundlehren der mathematischen Wissenschaften, Band 114, Springer-Verlag, Berlin-New York, 1967. MR 0349792
- D. G. Northcott, An introduction to homological algebra, Cambridge University Press, New York, 1960. MR 0118752
- I. B. S. Passi, Dimension subgroups, J. Algebra 9 (1968), 152–182. MR 231916, DOI 10.1016/0021-8693(68)90018-5
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 162 (1971), 15-25
- MSC: Primary 20.50; Secondary 18.00
- DOI: https://doi.org/10.1090/S0002-9947-71-99968-5