On the cohomology of split extensions

of finite groups

Author:
Stephen F. Siegel

Journal:
Trans. Amer. Math. Soc. **349** (1997), 1587-1609

MSC (1991):
Primary 20J06

DOI:
https://doi.org/10.1090/S0002-9947-97-01747-9

MathSciNet review:
1376556

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a split extension of finite groups. A theorem of Charlap and Vasquez gives an explicit description of the differentials in the Lyndon-Hochschild-Serre spectral sequence of the extension with coefficients in a field . We generalize this to give an explicit description of all the () in this case. The generalization is obtained by associating to the group extension a new twisting cochain, which takes values in the -endomorphism algebra of the minimal -projective resolution induced from to . This twisting cochain not only determines the differentials, but also allows one to construct an explicit -projective resolution of .

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Additional Information

**Stephen F. Siegel**

Email:
siegel@math.umass.edu

DOI:
https://doi.org/10.1090/S0002-9947-97-01747-9

Received by editor(s):
October 30, 1995

Additional Notes:
The author was supported by a Sloan Foundation dissertation fellowship and a National Science Foundation postdoctoral fellowship.

Article copyright:
© Copyright 1997
American Mathematical Society