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Witt classes of integral representations of an abelian $ 2$-group


Author: David E. Gibbs
Journal: Proc. Amer. Math. Soc. 70 (1978), 103-108
MSC: Primary 57R85; Secondary 10C05, 15A63, 20C10
DOI: https://doi.org/10.1090/S0002-9939-1978-0492055-1
MathSciNet review: 492055
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Abstract: In this paper the Witt groups of integral representations of an abelian 2-group $ \pi ,{W_0}(\pi ;Z)$ and $ {W_2}(\pi ;Z)$ are calculated. Invariants are listed which completely determine $ {W_0}({Z_4};Z)$ and $ {W_2}({Z_4};Z)$ and can be extended to the case $ \pi = {Z_{{2^k}}}$. If $ \pi $ is an elementary abelian 2-group, it is shown that $ {W_2}(\pi ;Z) = 0$ and $ {W_0}(\pi ;Z[\tfrac{1}{2}])$ is ring isomorphic to the group ring $ W(Z[\tfrac{1}{2}])({\operatorname{Hom}}(\pi ,{Z_2}))$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0492055-1
Keywords: Bordism, representation, Witt ring
Article copyright: © Copyright 1978 American Mathematical Society

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