Schur Lemmas, Part 1

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Group Direct Sums in Group Theory

Explores direct sums in group theory, focusing on abelian groups and their implications.

The Lemma of the Five: Abelian Groups

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

Abelian Groups: Technical Lemmas

Covers technical lemmas on abelian p-groups and maximal order elements.

Applications of Lagrange's Theorem

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

Useful Variants on Beta Action

Covers abelian groups, Sylow subgroups, and variants on beta action.

Functor Hom: Abelian Groups

Explores the Hom functor in Abelian groups, focusing on its construction and properties.

Torsion and Divisibility: Abelian Groups

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

Sylow Subgroups: Group Theory

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

Torsion and Divisibility in Group Theory

Explores the relationship between p-torsion and p-divisibility in group theory, highlighting implications of p-divisibility in exact sequences of abelian groups.

Direct Sums: Abelian Groups

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.