Lecture
This lecture introduces the concept of solvable groups, defined as groups that have a finite sequence of subgroups ending with the whole group, where each subgroup is normal in the previous one and the factor groups are abelian. The instructor explains how solvability can be understood as decomposing a group into abelian pieces. Various examples and properties of solvable groups are discussed, including different ways of decomposing them into subgroups. The lecture also covers the relationship between solvable groups and abelian factor groups, providing a deeper insight into the structure of groups.