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Lecture
Quotient Groups and Homomorphisms
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Related lectures (32)
Isomorphism Theorems: Quotients of Group
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Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.
Group Homomorphisms: Kernels, Images, and Normal Subgroups
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Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.
Active Learning: Group Homomorphisms
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Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.
Universal Property of Groups
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Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.
Groups and Products
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Covers the concepts of groups, products, and homomorphisms, focusing on the hx set and group alternates.
Applications of Lagrange's Theorem
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Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.
Homomorphisms: Birational Maps and Affine Varieties
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Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.
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.
Quotient Groups: Homomorphisms and Isomorphisms
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Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.
Quotients in Abelian Groups
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Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.
Groups & Rings: Morphisms, Kernels, and Injectivity
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Explores group morphisms, kernels, and injectivity in group theory.
Group Theory: Subgroups and General Group Actions
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Explores group actions, defining functors on groups, and verifying properties of group actions.
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