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Skew Tensor Products and Groups of Class Two

Published online by Cambridge University Press:  22 January 2016

Paul Conrad
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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
Information
Nagoya Mathematical Journal , Volume 23 , December 1963 , pp. 15 - 51
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

[1] Baer, R., Groups with abelian central quotient groups, Trans. Amer. Math. Soc, 44 (1938), pp. 357–386.CrossRefGoogle Scholar
[2] Baer, R., Groups with preassigned central and central quotient groups, Trans. Amer. Math. Soc, 44 (1938), pp. 387–412.Google Scholar
[3] Conrad, P., Completions of groups of class 2, Illinois J. Math. 5 (1961), pp. 212–224.Google Scholar
[4] Fuchs, L., Abelian groups, Budapest (1958).Google Scholar