Nondegenerate symmetric bilinear forms on finite abelian $2$-groups
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- by Rick Miranda PDF
- Trans. Amer. Math. Soc. 284 (1984), 535-542 Request permission
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.References
- Akio Kawauchi and Sadayoshi Kojima, Algebraic classification of linking pairings on $3$-manifolds, Math. Ann. 253 (1980), no. 1, 29–42. MR 594531, DOI 10.1007/BF01457818
- C. T. C. Wall, Quadratic forms on finite groups, and related topics, Topology 2 (1963), 281–298. MR 156890, DOI 10.1016/0040-9383(63)90012-0
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 284 (1984), 535-542
- MSC: Primary 20K10; Secondary 11E39
- DOI: https://doi.org/10.1090/S0002-9947-1984-0743731-1
- MathSciNet review: 743731