Groups: Definitions, Properties, and Homomorphisms

This lecture covers the fundamental concepts related to groups, including definitions, properties, and homomorphisms. It starts by defining a group as a set with a binary operation satisfying specific axioms. The lecture then explores the order of a group, abelian groups, and cyclic groups. It delves into topics such as the kernel of a homomorphism, generators of a group, and subgroup properties. Additionally, it discusses normal subgroups and their significance in group theory. The lecture concludes with examples of group homomorphisms and their applications in understanding group structures.