Groups & Subgroups: Definitions, Theorems, and Morphisms

Related lectures (28)

Page 2 of 3

Explores subsets and subgroups related to group actions on sets.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

Covers commutative groups and their significance in cryptography.

Covers natural transformations between functors, identity transformations, and equivalence of categories.

Covers subgroups, generators, cyclic groups, and group morphisms in group theory.

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

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

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Covers examples of categories like sets, groups, and vector spaces, exploring composition and product formation.

Explores group actions, defining functors on groups, and verifying properties of group actions.