Group Theory Basics

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Related lectures (51)

Group Actions: Theory and Examples Log in to Mediaspace to watch this video

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

RSA Encryption: Main Concepts Log in to Mediaspace to watch this video

Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.

Group Homomorphisms Log in to Mediaspace to watch this video

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

Groupes résolubles Log in to Mediaspace to watch this video

Explores solvable groups, group actions, normalizers, and stabilizers in group theory.

Categorical Perspective: Group Quotients Log in to Mediaspace to watch this video

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Group Theory: Quotients of Group Log in to Mediaspace to watch this video

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Motivations for studying group actions Log in to Mediaspace to watch this video

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

Hom Functor: Abelian Groups Log in to Mediaspace to watch this video

Explores the Hom functor for abelian groups and its relation to direct sums.

Functors and Homomorphisms in Group Theory Log in to Mediaspace to watch this video

Explores functors F_{Ab} and Hom (-,-) in group theory, including presentations and homomorphisms.

Quotient Groups: Homomorphisms and Isomorphisms Log in to Mediaspace to watch this video

Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.

Direct Sums Arithmetic Log in to Mediaspace to watch this video

Explores the arithmetic of direct sums in group theory, discussing conditions for equality.

Group Homomorphisms: Kernels, Images, and Normal Subgroups Log in to Mediaspace to watch this video

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

Linear Representations: Basics and Examples Log in to Mediaspace to watch this video

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

Group Homomorphisms Log in to Mediaspace to watch this video

Explores group homomorphisms, isomorphisms, and generators in abstract algebra.

Advanced Design of Concrete Structures Log in to Mediaspace to watch this video

Delves into advanced concrete structure design, covering loads, slabs, beams, calculations, and corbel models.

Group Theory: Active Learning Session Log in to Mediaspace to watch this video

Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.

Sylow Subgroups: Group Theory Log in to Mediaspace to watch this video

Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.

Quotients of Groups by Relations of Equivalence Log in to Mediaspace to watch this video

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

Finite Fields and Group Theory Log in to Mediaspace to watch this video

Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].

Equivalences of Categories Log in to Mediaspace to watch this video

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

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