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On the homology of split extensions with $p$-elementary kernel


Author: Marcin Chalupnik
Journal: Proc. Amer. Math. Soc. 129 (2001), 3143-3149
MSC (2000): Primary 20J06
DOI: https://doi.org/10.1090/S0002-9939-01-05987-1
Published electronically: April 16, 2001
MathSciNet review: 1844986
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Abstract:

We study a Hochschild-Serre spectral sequence associated to a split group extension with kernel $({\mathbf Z/p})^n$. It is shown that a large part of $E^{0*}_2$ must survive to infinity. We also sketch the general procedure of computing this surviving group.


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  • [Be1] S. Betley, Calculations in THH-Theory, J. Algebra 180, (1996), 445-458. MR 97a:19002
  • [Be2] S. Betley, Stable $K$-Theory of Finite Fields, $K$-Theory 17 (1999), 103-111. MR 2000d:18006
  • [dCP] C. de Concini, C. Procesi, A characteristic free approach to invariant theory, Advances in Math. 21 (1976), no. 3, 330-354. MR 54:10305
  • [EF] L. Evens, E. Friedlander, On $K_*(Z/p^2)$ and related homology groups, Trans. Amer. Math. Soc. 270 (1982), 1-46. MR 83j:18013
  • [Go] T. Goodwillie, Relative algebraic K-theory and cyclic homology, Ann. Math. 124 (1986), 347-402. MR 88b:18008
  • [HM] L. Hesselholt, I. Madsen, On the $K$-theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997), 29-101. MR 97i:19002
  • [Qu1] D. Quillen, On the cohomology and $K$-theory of the general linear groups over a finite field, Ann. Math. 96 (1972), 552-586. MR 47:3565
  • [Qu2] D. Quillen, Characteristic classes of representations, Lect. Notes in Math. 551, (1976) (189-216). MR 58:28215
  • [Sa] C.-H. Sah, Cohomology of split extensions, J. Algebra 29 (1974), 255-302. MR 52:14083

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Additional Information

Marcin Chalupnik
Affiliation: Instytut Matematyki, University of Warsaw, ul. Banacha 2, 02–097 Warsaw, Poland
Email: mchal@mimuw.edu.pl

DOI: https://doi.org/10.1090/S0002-9939-01-05987-1
Received by editor(s): August 25, 1999
Received by editor(s) in revised form: March 8, 2000
Published electronically: April 16, 2001
Additional Notes: The author was partially supported by the Polish scientific grant (KBN) 2 P03A 01113
Communicated by: Ralph Cohen
Article copyright: © Copyright 2001 American Mathematical Society

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