Solvable Groups: Part 1

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Groupes résolubles: Quotients and Subgroups

Explores the concept of solvable groups and their subgroups' impact on solvability.

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Symmetry and Group Theory

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

Subgroups and Cosets: Lagrange's Theorem

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

Subsets and subgroups associated with an action

Explores subsets and subgroups related to group actions on sets.

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.

Automorphism Groups: Trees and Graphs III

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

Finite Abelian Groups

Covers Cauchy's theorem, classification of finite abelian groups, direct product properties, and more.

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.

Applications of Lagrange's Theorem

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