Group Theory Basics: Subgroups and Homomorphisms

Related lectures (53)

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

Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.

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

Explores Lagrange's theorem applications in group theory and arithmetic, focusing on subgroups, cosets, quotient groups, and homomorphisms.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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