Lectures related to Lagrange Theorem: Equivalence Relations

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

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

Covers commutative groups and their significance in cryptography.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

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

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Covers technical lemmas on abelian p-groups and maximal order elements.

Explores isomorphic groups, bijective morphisms, and their applications in group theory.

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Explores character representations in group repetition theory, discussing irreducibility, equivalence, and associated values.

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Explores cardinality in sets and properties of groups, including commutativity and examples of abstract groups.

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Delves into advanced group theory concepts such as isomorphisms and homomorphisms.

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

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.