Given two normal subgroups G_1 and G_2 of a group, and two normal subgroups H_1 and H_2 of G_1 and G_2 respectively, H_1(G_1 intersection H_2) is normal in H_1(G_1 intersection G_2) (H_1 intersection G_2) H_2 is normal in (G_1 intersection G_2) H_2, and one has an isomorphism of quotient groups H_1(G_1 intersection G_2)/H_1(G_1 intersection H_2)≃(G_1 intersection G_2) H_2/(H_1 intersection G_2) H_2 (Zassenhaus 1934). This lemma was named by Serge Lang based on the shape of the diagram above, which Lang derived from Zassenhaus's original publication.

butterfly catastrophe | butterfly curve | butterfly effect | butterfly function | butterfly graph | butterfly polyiamond | butterfly theorem | composition series | Hasse diagram | Jordan-Hölder theorem

moths and butterflies