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Lecture
Abelian Groups: Technical Lemmas
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Related lectures (52)
Direct Sums Arithmetic
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Explores the arithmetic of direct sums in group theory, discussing conditions for equality.
Categorical Perspective: Abelian Groups
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Explores abelian groups from a categorical perspective, discussing the coproduct construction.
Orbit-Stabilizer Theorem: Conjugacy Classes and Direct Products
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Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.
The Lemma of the Five: Abelian Groups
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Presents the Lemma of the Five, a fundamental result in group theory.
Torsion and Divisibility in Group Theory
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Explores the relationship between p-torsion and p-divisibility in group theory, highlighting implications of p-divisibility in exact sequences of abelian groups.
Existence of Direct Sums: Abelian Groups
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Demonstrates the existence of direct sums of abelian groups and covers propositions and proofs related to their uniqueness.
Hom Functor: Abelian Groups
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Explores the Hom functor for abelian groups and its relation to direct sums.
Finite Fields and Group Theory
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Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].
Sylow Subgroups: Group Theory
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Explores the concept of p-subgroups of Sylow in group theory, emphasizing the philosophy of studying mathematical objects 'one prime at a time'.
Galois Theory: Solvability and Radical Extensions
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Explores solvability by radicals in Galois theory and the Galois/Abel criterion for solvability.
Groupes résolubles
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Explores solvable groups, group actions, normalizers, and stabilizers in group theory.
Monster Group: Representation
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Explores the Monster group, a sporadic simple group with a unique representation theory.
Characters and Dirichlet's Theorem
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Introduces characters over a finite abelian group and explains the proof of the infinitude of primes in arithmetic progressions.
Group Operations and Homomorphisms in Abelian Groups
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Explores operations on abelian groups, Homomorphisms, adjoints, and morphisms in group theory.
Symmetric Group: Cycle Notation
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Explores the symmetric group, emphasizing cycle notation and group properties.
Group Theory: Isomorphism and Semi-Direct Product
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Covers group theory concepts like isomorphism and semi-direct product through examples and proofs.
Group Theory Basics
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Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.
Quotients of Groups by Relations of Equivalence
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Explores quotients of groups by equivalence relations and the conditions for well-defined sets.
Cardinality and Group Theory
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Explores cardinality in sets and properties of groups, including commutativity and examples of abstract groups.
Quotient Groups: Homomorphisms and Isomorphisms
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Explores quotient groups, homomorphisms, isomorphisms, and push-outs in different categories.
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