For F a field and G a group, let
FG denote the group algebra of G over F. Let 𝒢 be a class of finite groups. Call the
fields F and F equivalent on 𝒢 if for all G,H ∈𝒢, FG ≃ FH if and only if
FG ≃FH. In [9] we began a study of this equivalence relation, discussing the case
when 𝒢 consists of alI finite p-groups, for p an odd prime. In this note we continue
our study of the equivalence relation. Section one deals with some general
results, section two solves the equivalence problem when 𝒢 is the class of all
finite 2-groups, and some remarks about the results are made in section
three.
