Self-similar Groups: Invariance and Structure

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Page 3 of 4

Recap of Group Theory

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Two Definitions of Group Action

Explores two definitions of group action on a set, focusing on properties and applications.

Active Learning: Group Theory

Explores adjoint functors, points fixes, orbits, and non-trivial actions in group theory.

Endomorphisms and automorphisms of totally disconnected locally compact groups

Explores endomorphisms and automorphisms of totally disconnected locally compact groups, emphasizing the properties of flat groups and free abelian subgroups.

Resoluble Groups: Quotients of Group

Covers the definition of solvable groups and the abelian property of group quotients.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Groupes résolubles

Explores solvable groups, group actions, normalizers, and stabilizers in group theory.

Finite Abelian Groups: Classification Theorem

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

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.

Symmetry and Group Theory: Exercise Set 4

Explores symmetry operations, isomorphic representations, and three-dimensional group representations.