Symmetric Group and Alternating Group

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Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.

Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.

Covers symmetric groups, transpositions, sign of a permutation, and conjugacy classes in permutations.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

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

Explores automorphism groups of trees and graphs, including actions on trees and group homomorphisms.

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.