I'm sure you omitted this just because it's too classic: big part of group theory was invented to prove that most roots of unity cannot be constructed by quadratic (or cyclic) extensions.

It's still the best, most direct connection between [nt.number-theory] and [gr.group-theory] I know of.

For a more "advanced" version of this, do computations of group cohomology count?

I'm sure you omitted this just because it's too classic: big part of group theory was invented to prove that most algebraic numbers cannot be constructed by radical extensions.

It's still the best, most direct connection between [nt.number-theory] and [gr.group-theory] I know of.

For a more "advanced" version of this, do computations of group cohomology count?

I'm sure you omitted this just because it's too classic: big part of group theory was invented just to prove that most roots of unity cannot be constructed by quadratic extensions. Yet it's still a very good example.

I'm sure you omitted this just because it's too classic: big part of group theory was invented to prove that most roots of unity cannot be constructed by quadratic (or cyclic) extensions.

It's still the best, most direct connection between [nt.number-theory] and [gr.group-theory] I know of.

For a more "advanced" version of this, do computations of group cohomology count?