Covers group theory fundamentals, motivations for studying group actions, equivalent definitions, and subsets associated with group actions.
Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.
Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.
Explores the arithmetic of direct sums in group theory, discussing conditions for equality.
Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.
Delves into the second isomorphism theorem in group theory, emphasizing subgroup relationships and quotient groups.
Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.
Covers the concept of group presentations using generators and relations to define groups.
