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Lecture
Motivations for studying group actions
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Related lectures (55)
Group Actions: Examples and Applications
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Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.
Direct Products in Group Theory
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Explores direct products in group theory, including semi-direct products and group properties.
Categorical Perspective: Abelian Groups
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Explores abelian groups from a categorical perspective, discussing the coproduct construction.
Abelian Groups: Free Abelian Groups
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Explores free abelian groups, homomorphisms, and exact sequences in group theory.
Untitled
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Active Learning: Group Homomorphisms
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Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.
Morphism of Groups
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Covers the concept of morphism of groups, actions on sets, and automorphisms.
Hom Functor: Abelian Groups
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Explores the Hom functor for abelian groups and its relation to direct sums.
Group Homomorphisms
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Explores group homomorphisms, isomorphisms, and generators in abstract algebra.
Functors and Homomorphisms in Group Theory
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Explores functors F_{Ab} and Hom (-,-) in group theory, including presentations and homomorphisms.
Diffeomorphism and implicit functions
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Explores diffeomorphisms, implicit functions, and coordinate transformations in advanced analysis.
Quotient Groups: Homomorphisms and Isomorphisms
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Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.
Symmetric Group: Cycle Notation
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Explores the symmetric group, emphasizing cycle notation and group properties.
Group Operations and Homomorphisms in Abelian Groups
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Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.
The Torus and Linear Groups
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Explores the torus, linear groups, stability properties of matrices, and homomorphisms.
Group Theory: Quotients of Group
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Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.
Categorical Perspective: Group Quotients
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Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.
Quotients of Groups by Relations of Equivalence
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Explores quotients of groups by equivalence relations and the conditions for well-defined sets.
Applications of Lagrange's Theorem
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Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.
Endomorphisms: Matrix Equivalence
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Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.
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