Applications of Lagrange's Theorem

This lecture delves into the applications of Lagrange's theorem in algebra, exploring corollaries related to the order of elements in finite groups, such as the divisibility of group orders and the existence of cyclic groups. The lecture also covers Euler's theorem, Fermat's Little theorem, and the classification of groups of order less than or equal to 5. Additionally, the concept of quotient groups and normal subgroups is introduced, showcasing how left cosets form a group under certain conditions. Examples and proofs are provided to illustrate the theoretical concepts discussed.