Nondegenerate symmetric bilinear forms on finite abelian -groups
Author: Rick Miranda
Journal: Trans. Amer. Math. Soc. 284 (1984), 535-542
MSC: Primary 20K10; Secondary 11E39
MathSciNet review: 743731
Abstract: Let be the semigroup of isomorphism classes of finite abelian -groups with a nondegenerate symmetric bilinear form having values in . Generators for 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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-  C. T. C. Wall, Quadratic forms on finite groups, and related topics, Topology 2 (1963), 281–298. MR 0156890, https://doi.org/10.1016/0040-9383(63)90012-0