Finite Abelian GroupsCovers Cauchy's theorem, classification of finite abelian groups, direct product properties, and more.
Group Algebra: Maschke's TheoremExplores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Finite Abelian Groups & RingsExplores the classification of finite abelian groups and rings, emphasizing elementary divisors and properties of rings.
Conjugation in GroupsExplores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.
Symmetry and Group TheoryExplores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.
Direct Sums: Abelian GroupsExplores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.