Group Theory: Properties and Examples

Related lectures (31)

Page 3 of 4

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Introduces group theory concepts, properties, and examples, including injective functions and group properties like associativity and inverses.

Explores the concept of free abelian groups as an important left adjoint functor.

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

Covers subsets in group theory and Lagrange's theorem with examples.

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Explores group theory in quantum physics, emphasizing reducible and irreducible representations, conservation laws, and group properties.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.

Explores symmetries in plane geometry, including isometries, reflections, and practical applications in design.