Vanishing homology over nilpotent groups
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- by William G. Dwyer PDF
- Proc. Amer. Math. Soc. 49 (1975), 8-12 Request permission
Abstract:
Let $\pi$ be a nilpotent group and let $M$ be a $\pi$-module. Under certain finiteness assumptions we prove that the twisted homology groups ${H_i}(\pi ,M)$ vanish for all positive $i$ whenever ${H_0}(\pi ,M) = 0$.References
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573 W. Dwyer, Generalized convergence of the Eilenberg-Moore spectral sequence (in preparation). E. Dror, Homology circles (in preparation). S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
- Tadasi Nakayama, On modules of trivial cohomology over a finite group, Illinois J. Math. 1 (1957), 36–43. MR 84014
- Donald S. Passman, Infinite group rings, Pure and Applied Mathematics, vol. 6, Marcel Dekker, Inc., New York, 1971. MR 0314951
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 49 (1975), 8-12
- MSC: Primary 18H10; Secondary 55H20
- DOI: https://doi.org/10.1090/S0002-9939-1975-0374242-3
- MathSciNet review: 0374242