D. - S. Kang, Z. Reichstein, Trace forms of
Galois field extensions
in the presence of roots of unity
, J. Reine Angew. Math., 549 (2002), 79--89.
Let L/K be a G-Galois field extension
and let G_2 be a Sylow subgroup of G.
We show that if G_2 is not abelian then the trace form
of L/K is hyperbolic, provided that K contains
certain roots of unity.