Definition: Understanding Group Structures

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Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Universal Property of Groups

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

Abelian p-groups: Groupes abéliens

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Coxeter Groups: Classification Theorem & Order of F_4

Explores the classification theorem for Coxeter groups and the order of F_4.

Lagrange's Theorem: Applications and Homomorphisms

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Permutations and Adjacency

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.

Sylow Subgroups: Structure and Properties

Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.

Covers self-similar groups and automorphisms of rooted trees, exploring residually finite groups and congruence subgroups.

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.

Subgroups and Generators

Covers subgroups, generators, cyclic groups, and group morphisms in group theory.