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Centralizer, normalizer, and center
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Related lectures (47)
Subsets and subgroups associated with an action
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Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.
Groups: Definitions, Properties, and Homomorphisms
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Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.
Group Theory Fundamentals
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Introduces group theory basics and group action concepts with associated subsets.
Universal Property of Groups
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Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.
Direct Sums Arithmetic
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Explores the arithmetic of direct sums in group theory, discussing conditions for equality.
Torsion and Divisibility: Abelian Groups
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Introduces torsion and divisibility concepts in abelian groups to describe their structure.
Active Learning: Group Homomorphisms
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Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.
Groups & Rings: Morphisms, Kernels, and Injectivity
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Explores group morphisms, kernels, and injectivity in group theory.
Lagrange's Theorem: Applications and Homomorphisms
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Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.
Diagonalizable Groups
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Explores the concept of diagonalizable groups and their properties in linear algebraic groups.
Connected Components
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Covers the concept of connected components in linear algebraic groups and their relationship to singular groups.
Equidistribution of CM Points
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Explores the joint equidistribution of CM points and their properties in ergodic theory and homogeneous dynamics.
Monstrous Moonshine
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Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.
Class Equation and Burnside's Lemma
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Explores the class equation and Burnside's lemma in group theory.
Geometric Quantization: Representation Theory
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Explores geometric quantization in representation theory, focusing on SO3(R) acting on R³ and homogenous polynomials.
Homomorphism of Groups: Signature
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Explores homomorphisms of groups, focusing on the signature sgn and the concept of cycles and transpositions.
Coxeter Groups: Generators and Relations
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Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.
Finite Abelian Groups: Classification Theorem
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Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.
Morphism of Groups
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Covers the concept of morphism of groups, actions on sets, and automorphisms.
The Lemma of the Five: Abelian Groups
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Presents the Lemma of the Five, a fundamental result in group theory.
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