Explore the intriguing connections between elimination of generators and various combinatorial theories in this 46-minute lecture by Gérard Duchamp from Paris-North University. Delve into topics such as bisection and codes, semidirect products of presented groups and Lie algebras, strange gradings over semigroups, and Lazard elimination. Discover unifying categorical links between these theories and learn general results that enable quick identification of semidirect decompositions. Gain insights from this collaborative work with Paul-André Melliès and Vu Nguyen Dinh, presented at the Institut des Hautes Etudes Scientifiques (IHES).