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Two remarks on the homology of group extensions

Published online by Cambridge University Press:  09 April 2009

Peter Hilton  and
Urs Stammbach
Peter Hilton
Affiliation:
Battelle Seattle Research Center, University of Washington, Seattle, ETH, Zurich, Switzerland
Urs Stammbach
Affiliation:
Battelle Seattle Research Center, University of Washington, Seattle, ETH, Zurich, Switzerland
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In this note we apply a particular technique to obtain information on the homology homomorphism ε*: H*(G; A) → H* (Q; A) associated with a group extension and a Q-module A. The technique consists of using ε itself to pull-back (0.1); that is, we construct the pull-back extension induced from (0.1) by ε. This, however, is nothing but the semidirect product, NG, of N and G, with G operating on the left on N by conjugation. Thus we obtain from (0.1) the commutative diagram where ε1 is the projection and et is the multiplication ε1(n, x) = nx,n∈N,x∈G. We now apply the Lyndon-Hochschild-Serre spectral sequence functor to (0.2) and carry out computations in dimensions 2 and 3.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 3 , May 1974 , pp. 345 - 357
Copyright
Copyright © Australian Mathematical Society 1974

References

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