Variable G : {group gT}.

(* Specifications: *)
Lemma index_cent1 x : #|G : 'C_G[x]| = #|x ^: G|.
Lemma abelian_classP : reflect {in G, forall x, x ^: G = [set x]} (abelian G).
Lemma card_classes_abelian : abelian G = (#|classes G| == #|G|).
End CardClass.