Concept

Group isomorphism problem

Related lectures (19)

Isomorphism in Aut(p)

Explores isomorphism between Aut(p) and a Galois covering through topology course notes.

Isomorphism: Order of Group Elements

Explores isomorphism and the order of group elements, emphasizing matching identities and inverses.

Group Theory: Isomorphism and Semi-Direct Product

Covers group theory concepts like isomorphism and semi-direct product through examples and proofs.

Finitely Generated Abelian Groups

Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.

Group Theory: Part 2

Delves into advanced group theory concepts such as isomorphisms and homomorphisms.

Isomorphism Theorems: Third Isomorphism Theorem

Explores the third isomorphism theorem in group theory, focusing on quotient groups and a categorical perspective.

Applications of Lagrange's Theorem

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Pushouts in Group Theory: Universal Properties Explained

Covers the construction and universal properties of pushouts in group theory.

Commutative Groups: Foundations for Cryptography

Covers commutative groups and their significance in cryptography.

Morphism of Groups

Covers the concept of morphism of groups, actions on sets, and automorphisms.

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.