Applications of Lagrange's Theorem

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Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Explores examples of group actions on sets, emphasizing the utility of group actions to understand groups.

Explores the symmetric group, emphasizing cycle notation and group properties.

Explores group homomorphisms, emphasizing surjective mappings and their impact on group questions.

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

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

Introduces group theory basics and group action concepts with associated subsets.

Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.

Covers explicit calculations of push-outs in Ens and the study of induced homomorphisms between quotient groups.

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Explores group morphisms and determinants in K-vector spaces.

Explores embeddings of number fields, types, signatures, lattices, and determinants.

Explores the construction of the Fischer-Greiss monster group, emphasizing its key properties and the process involved.

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