Section CenterMode.
Variable i : sG.
Let i0 := Ordinal (irr_degree_gt0 i).
Definition irr_mode x := irr_repr i x i0 i0.
End CenterMode.

Lemma splitting_cyclic_primitive_root :
cyclic G -> [char F]^'.-group G -> group_splitting_field G ->
classically {z : F | #|G|.-primitive_root z}.