Group isomorphism problem

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Second Isomorphism Theorem

Delves into the second isomorphism theorem in group theory, emphasizing subgroup relationships and quotient groups.

Equivalences of Categories

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

First Isomorphism Theorem

Covers the first isomorphism theorem in group theory and its applications.

Group Homomorphisms

Explores group homomorphisms, Euler's phi function, and group products.

Subrepresentations of the regular representation

Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.

Diffie-Hellman and ElGamal Cryptosystems

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Symmetry and Group Theory

Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.

Linear Lie Groups: Definitions and Theorems

Discusses linear Lie groups, their definitions, properties, and the relationship between integral curves and vector fields.

Topology: Fundamental Groups and Applications

Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.