Equivalence of Unimodular (Quadratic)forms on Abelian groups

[WWGD]

Hi, everyone:

I have been looking for a while without success, for the definition of equivalence for
unimodular quadratic forms defined on Abelian groups .
I have found instead ,t the def. of equivalence in the more common case where the two forms Q,Q' are defined on vector spaces , and the definition has to see with matrices
in Sl_n(Z) . It makes sense that the equivalence of unimodular forms has to see with
matrices in Sl_n(Z) , since these have determinant +/- 1 . But it is not too clear to me
how we would define this equivalence if instead we had Q,Q' unimodular ,defined on Abelian groups A,A' respectively. Anyone know?.

Thanks.

 

[fresh_42]

I'm not sure, but I would consider group algebras like $\mathbb{Z}[A]$ to get the two different operations needed.