MATH-211: Algebra II - groups

Lectures in this course (52)

Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.

Explores the concept of free abelian groups as an important left adjoint functor.

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

Covers exact sequences of homomorphisms in abelian groups, including injective sequences and split sequences.

Presents the Lemma of the Five, a fundamental result in group theory.

Introduces torsion and divisibility concepts in abelian groups to describe their structure.

Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.

Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.

Explores the study of finite groups through subgroup analysis, focusing on Sylow subgroups.

Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.

Explores the beautiful properties of the p-Sylow subgroups of a finite group.

Explores the properties of p-subgroups of Sylow in a group.

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