Arithmetic equivalence under isoclinism.

Two algebraic number fields are called arithmetically equivalent if the Dedekind zeta functions of the fields coincide. We show that if a G-extension contains non-conjugate arithmetically equivalent fields and there is an injection from G to another group H inducing an isoclinism between G and H, then there are non-conjugate arithmetically equivalent fields inside an H-extension. [ABSTRACT FROM AUTHOR]