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Covers the concept of solvable groups and their decomposition into abelian pieces, exploring various properties and examples.
Explores vector valued functions, their representations, uniqueness, and congruence subgroups.
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.
Covers group theory fundamentals, motivations for studying group actions, equivalent definitions, and subsets associated with group actions.
Covers the group presentation of S3, normal subgroups, generators, relations, quotient groups, and injective homomorphisms.
Delves into the second isomorphism theorem in group theory, emphasizing subgroup relationships and quotient groups.
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Covers the concept of group presentations using generators and relations to define groups.
Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.
