Commutator subgroup

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Related lectures (31)

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Abelianization of Fundamental Group

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

The Degree of a Covering Space

Shows the equivalence between the index of a covering space's fundamental group and the degree of the covering space.

Hidden Sub-group Problem and Simon Algorithm

Explores the hidden sub-group problem and Simon algorithm in quantum computing.

Isomorphism Theorems: Third Isomorphism Theorem

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

Cohomology: Cup Product

Covers the cup product in cohomology, focusing on examples and computations.

Cryptography and Information Theory

Explores cryptography, perfect secrecy, group theory, and modern cryptographic milestones, emphasizing the trade-off between security and cost.

Quotients of Linear Groups by Linearly Reductive Groups

Explores constructing quotients of linear algebraic groups by linearly reductive sub-groups.

Normal Subgroups and Quotients

Introduces normal subgroups, group quotients, and their applications in group theory.

Quantum Physics I

Introduces key quantum physics concepts such as commutators, observables, and the Schrödinger equation, emphasizing the importance of diagonalization and energy eigenvalues.

Subgroups and subalgebras

Explores the unique determination of homomorphisms by differentials and the intersection of closed subgroups' Lie algebras.