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Learn the fundamental concepts of group theory in abstract algebra through this comprehensive video series spanning over 6 hours. Master the definition of groups and explore basic examples before progressing to general group properties and the group of units modulo n. Understand subgroups through the subgroup test and examine the center of a group, coset equality, and Lagrange's Theorem. Dive into group isomorphisms and their properties, including the classification of cyclic groups with numerous practical examples. Explore advanced topics such as Cayley's Theorem, direct products of groups, and internal direct products of subgroups. Study group homomorphisms, normal subgroups, and quotient groups, including specific applications to quaternions. Investigate the relationship between quotient groups and centers, homomorphisms and element order, and kernels of homomorphisms. Master the three fundamental isomorphism theorems for groups with practical applications, and conclude with inner automorphisms and advanced theorem applications.
