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Skew Tensor Products and Groups of Class Two

Published online by Cambridge University Press:  22 January 2016

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Let Δ and N be abelian groups and let f be a mapping of Δ × Δ into N that is bilinear, skew symmetric and satisfies f(α, α) = 0 for all α ∈ Δ. Such a mapping f is called a (*)-mapping. By the Schreier extension theory Δ, N and f determine a nilpotent group G(Δ, N, f) of class two that consists of the set Δ × N with composition

(α, a) + (β, b) = (α + β, f(α, β) + a + b).

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

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