Lectures related to Groups and Numbers: Mathematical Elements on Groups

Natural Numbers: Properties and Operations

Explores natural numbers, their properties, operations, and practical applications like calculating hours in a year.

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Pushouts in Group Theory: Universal Properties Explained

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

Finitely Generated Abelian Groups

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Abelian Groups: First Approach

Introduces the theory of abelian groups, focusing on p-abelian groups and their structure.

Resoluble Groups: Quotients of Group

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

Direct Sums Arithmetic

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Group Repetition Theory: Character Representations

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