Existence of Sylow Subgroups: Proof by Recurrence

This lecture demonstrates the existence of p-Sylow subgroups in any finite group where the prime p divides the order. The proof, based on induction and reduction to the abelian case, follows the classification of finite abelian groups. The instructor shows how the class equation leads to the conclusion that p divides the order of the center of the group, crucial for establishing the existence of Sylow subgroups.