End MorphNil.
Section QuotientNil.
Variables gT : finGroupType.
Implicit Types (rT : finGroupType) (G H : {group gT}).

(* Specifications: *)
Lemma quotient_ucn_add m n G : 'Z_(m + n)(G) / 'Z_n(G) = 'Z_m(G / 'Z_n(G)).
Lemma isog_nil rT G (L : {group rT}) : G \isog L -> nilpotent G = nilpotent L.
Lemma nil_class_quotient_center G :
nilpotent (G) -> nil_class (G / 'Z(G)) = (nil_class G).-1.
Lemma nilpotent_sub_norm G H :
nilpotent G -> H \subset G -> 'N_G(H) \subset H -> G :=: H.
Lemma nilpotent_proper_norm G H :
nilpotent G -> H \proper G -> H \proper 'N_G(H).
Lemma nilpotent_subnormal G H : nilpotent G -> H \subset G -> H <|<| G.
Lemma TI_center_nil G H : nilpotent G -> H <| G -> H :&: 'Z(G) = 1 -> H :=: 1.
Lemma meet_center_nil G H :
nilpotent G -> H <| G -> H :!=: 1 -> H :&: 'Z(G) != 1.
Lemma cyclic_nilpotent_quo_der1_cyclic G :
nilpotent G -> cyclic (G / G^`(1)) -> cyclic G.