Section DerivedGroup.
Variable gT : finGroupType.
Implicit Types G H : {group gT}.

(* A non-trivial solvable group has a nonprincipal linear character. *)
Lemma solvable_has_lin_char G :
G :!=: 1%g -> solvable G ->
exists2 i, 'chi[G]_i \is a linear_char & 'chi_i != 1.