Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Vanishing homology over nilpotent groups

Author: William G. Dwyer
Journal: Proc. Amer. Math. Soc. 49 (1975), 8-12
MSC: Primary 18H10; Secondary 55H20
MathSciNet review: 0374242
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] 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
  • [2] W. Dwyer, Generalized convergence of the Eilenberg-Moore spectral sequence (in preparation).
  • [3] E. Dror, Homology circles (in preparation).
  • [4] S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
  • [5] Tadasi Nakayama, On modules of trivial cohomology over a finite group, Illinois J. Math. 1 (1957), 36–43. MR 0084014
  • [6] Donald S. Passman, Infinite group rings, Marcel Dekker, Inc., New York, 1971. Pure and Applied Mathematics, 6. MR 0314951

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 18H10, 55H20

Retrieve articles in all journals with MSC: 18H10, 55H20

Additional Information

Keywords: Nilpotent group, twisted group homology
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society