Concept

Identity element

Related lectures (26)

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers commutative groups and their significance in cryptography.

Covers the rapid decay of Whittaker functions for upsets, focusing on the assumption of Vize = 1.

Introduces the basics of group theory, including operations, properties, and Lie groups.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Covers the properties of linear molecules in carbon and discusses neutral elements, associative law, and conjugate elements.

Covers element by element operations in MATLAB and Octave for beginners.

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Covers the definitions and properties of vector spaces, including axioms and examples.

Covers group actions, bijections, evaluations, translations, homomorphisms, and inverses within universal actions.

Covers the basics of numerical modeling of solids and structures.

Covers the fundamental concepts of group theory and examples of real numbers and permutations.

Covers addition properties and operations in the set of integers Z.

Explores product groups and isomorphism between sets with different operations but the same structure.

Covers the basics of group theory, including definitions, examples, and isometries.

Covers properties and notation of the trivial group and discusses the uniqueness of elements.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

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

Covers the basics of group theory, including elements, associativity, identity, inverses, and closure.

Covers the definition of a group, properties of symmetries, and group operations.