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Some cancellation theorems

Part of: Basic linear algebra Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

A. R. Shastri
A. R. Shastri
Affiliation:
Tata Institute of Fundamental Research, Homi Bhabha Road Bombay 400 005, India
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Abstract

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If G, H and B are groups such that G × B ≃ H × B, G/[G, G]. Z(G) is free abelian and B is finitely generated abelian, then G ≃ H. The equivalence classes of triples (Vξ,A) where Vand A are finitely generated free abelian groups and ξ: V⊗ V → A is a bilinear form constitute a semigroup B undera natural external orthogonal sum. This semigroup B is cancellative. A cancellation theorem for class 2 nilpotent groups is deduced.

MSC classification

Secondary: 20F06: Cancellation theory; application of van Kampen diagrams 20F18: Nilpotent groups 15A63: Quadratic and bilinear forms, inner products
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 87 - 97
Copyright
Copyright © Australian Mathematical Society 1980

References

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