Published online by Cambridge University Press: 20 November 2018
For F a field and G a group, let FG = F(G) be the group algebra of G over F. It is a class of finite abelian groups, F induces an equivalence relation on
by
are equivalent if and only if FG ⋍ FH. We will call two fields F and K equivalent on
if they induce the same equivalence relation on
We will say F is equivalent to isomorphism on
if FG ⋍ FH if and only if G ⋍ H for any two elements
.