Definition: Understanding Group Structures

Related lectures (31)

Page 2 of 4

Explores cosets in commutative groups, Lagrange theorem, and integer factorization.

Covers the concept of solvable groups and their decomposition into abelian pieces, exploring various properties and examples.

Explores subsets and subgroups related to group actions on sets.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

Discusses the theory of free groups, their properties, and relationships with other algebraic structures.

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

Introduces subgroups and homomorphisms in group theory, with examples for illustration.