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Related lectures (29)

Page 3 of 3

Explores self-similar groups, invariance under section maps, closures, and topological structures in group theory.

Existence: Proof of Classification Theorem

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic groups.

Finite Fields and Group Theory

Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].

Algebra: Practice Exam Solutions

Covers the solution of a practice exam in Algebra, focusing on finding greatest common divisors of polynomials and exploring group properties.

Group Theory - Part 2

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Definition: Understanding Group Structures

Explores the philosophy of understanding a group through its subgroups' structure, focusing on finite groups.

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Discrete Log Problem: Pollard's Rho Method

Introduces Pollard's rho method for the discrete log problem and finding collisions efficiently in a cyclic group.

Applications of Lagrange's Theorem

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