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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Nondegenerate symmetric bilinear forms on finite abelian $ 2$-groups


Author: Rick Miranda
Journal: Trans. Amer. Math. Soc. 284 (1984), 535-542
MSC: Primary 20K10; Secondary 11E39
MathSciNet review: 743731
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Abstract: Let $ {\mathcal{B}_2}$ be the semigroup of isomorphism classes of finite abelian $ 2$-groups with a nondegenerate symmetric bilinear form having values in $ Q/{\mathbf{Z}}$. Generators for $ {\mathcal{B}_2}$ were given by C. T. C. Wall and the known relations among these generators were proved to be complete by A. Kawauchi and S. Kojima. In this article we describe a normal form for such bilinear forms, expressed in terms of Wall's generators, and as a by-product we obtain a simpler proof of the completeness of the known relations.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0743731-1
PII: S 0002-9947(1984)0743731-1
Article copyright: © Copyright 1984 American Mathematical Society