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, Springer, New York, 1972. MR 0365573 (51:1825)
  • [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] T. Nakayama, On modules of trivial cohomology over a finite group, Illinois J. Math. 1 (1957), 36-43. MR 18, 793. MR 0084014 (18:793e)
  • [6] D. Passman, Infinite group rings, Dekker, New York, 1971, p. 136. MR 0314951 (47:3500)

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