On the homology of split extensions with -elementary kernel

Author:
Marcin Chalupnik

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3143-3149

MSC (2000):
Primary 20J06

Published electronically:
April 16, 2001

MathSciNet review:
1844986

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We study a Hochschild-Serre spectral sequence associated to a split group extension with kernel . It is shown that a large part of must survive to infinity. We also sketch the general procedure of computing this surviving group.

**[Be1]**Stanislaw Betley,*Calculations in 𝑇𝐻𝐻-theory*, J. Algebra**180**(1996), no. 2, 445–458. MR**1378539**, 10.1006/jabr.1996.0076**[Be2]**Stanislaw Betley,*Stable 𝐾-theory of finite fields*, 𝐾-Theory**17**(1999), no. 2, 103–111. MR**1696427**, 10.1023/A:1007781714000**[dCP]**C. de Concini and C. Procesi,*A characteristic free approach to invariant theory*, Advances in Math.**21**(1976), no. 3, 330–354. MR**0422314****[EF]**Leonard Evens and Eric M. Friedlander,*On (𝐾_{∗}(𝑍/𝑝²𝑍) and related homology groups*, Trans. Amer. Math. Soc.**270**(1982), no. 1, 1–46. MR**642328**, 10.1090/S0002-9947-1982-0642328-X**[Go]**Thomas G. Goodwillie,*Relative algebraic 𝐾-theory and cyclic homology*, Ann. of Math. (2)**124**(1986), no. 2, 347–402. MR**855300**, 10.2307/1971283**[HM]**Lars Hesselholt and Ib Madsen,*On the 𝐾-theory of finite algebras over Witt vectors of perfect fields*, Topology**36**(1997), no. 1, 29–101. MR**1410465**, 10.1016/0040-9383(96)00003-1**[Qu1]**Daniel Quillen,*On the cohomology and 𝐾-theory of the general linear groups over a finite field*, Ann. of Math. (2)**96**(1972), 552–586. MR**0315016****[Qu2]**Daniel Quillen,*Characteristic classes of representations*, Algebraic K-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976) Springer, Berlin, 1976, pp. 189–216. Lecture Notes in Math., Vol. 551. MR**0578500****[Sa]**Chih Han Sah,*Cohomology of split group extensions*, J. Algebra**29**(1974), 255–302. MR**0393273**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
20J06

Retrieve articles in all journals with MSC (2000): 20J06

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