Group Theory: Combinatorial Approach

Related lectures (29)

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

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Introduces combinatorial group theory, emphasizing group presentations, normal subgroups, and group quotients.

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

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

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

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

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

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

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