Groupes résolubles: Quotients and Subgroups

This lecture explores the concept of solvable groups, focusing on the relationship between normal subgroups, quotient groups, and the solvability of the original group. The instructor presents Proposition 4.3, demonstrating that if both a group and its quotient by a normal subgroup are solvable, then the original group is also solvable. Through a series of proofs and examples, the lecture illustrates how the solvability of subgroups impacts the overall solvability of a group. The discussion delves into the categorical perspective on quotients, emphasizing the importance of understanding the structure of normal subgroups in determining the solvability of groups.