Lectures related to Lagrange's Theorem: Applications and Homomorphisms

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

Explores the symmetric group, emphasizing cycle notation and group properties.

Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

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

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Covers the concepts of groups, products, and homomorphisms, focusing on the hx set and group alternates.

Delves into push-out and quotients in group theory, emphasizing homomorphisms and normal subgroups.

Covers explicit calculations of push-outs in Ens and the study of induced homomorphisms between quotient groups.