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Abstract Kernels and Cohomology
Published online by Cambridge University Press: 09 April 2009
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Let G, N be groups, let A(N) be the automorphism group of N and let I(N) be the subgroup of inner automorphisms. A homomorphism θ: G → A(N)/I(N) will be denoted by (G, N, θ) and called an abstract kernel. (G, N, θ) induces in an obvious manner a structure of a (left) G-module on the centre C of N. A well known construction of Eilenberg and MacLane [1, § 7–9] assigns to (G, N, θ) its obstruction Obs (G, N, θ) ∈H3(G, C). This assignment is such that if C is an arbitrary G-module then every element of H3(G, C) is of the form Obs (G, N, θ) for a suitable abstract kernel (G, N, θ).
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- Copyright © Australian Mathematical Society 1968
References
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