Group Theory: Definitions and Properties

Related lectures (28)

Page 1 of 3

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Introduces group theory concepts, including definitions and properties of groups, rings, and fields.

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

Covers commutative groups and their significance in cryptography.

Explores the group structure and isomorphism of elliptic curves, including inverses, associativity, and compactification to the torus.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers the definition of a group, properties of symmetries, and group operations.

Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.