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Lecture
Abelian Groups: First Approach
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Related lectures (30)
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Abelian p-groups: Groupes abéliens
Focuses on abelian p-groups, demonstrating technical results for classifying finite abelian groups.
Symmetry and Group Theory
Explores chirality, group completeness, Abelian groups, conjugate classes, and isomorphic groups in symmetry and group theory.
Applications of Lagrange's Theorem
Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.
Existence of Sylow Subgroups: Proof by Recurrence
Demonstrates the existence of p-Sylow subgroups in any finite group using induction and the abelian case.
Abelian Groups: Technical Lemmas
Covers technical lemmas on abelian p-groups and maximal order elements.
Group Theory: Active Learning Session
Delves into group theory, emphasizing the centralizer of elements and the classification of finite abelian groups.
Sylow Subgroups: Structure and Properties
Explores the properties and structure of Sylow subgroups in group theory, emphasizing a theorem-independent approach.
Torsion and Divisibility: Abelian Groups
Introduces torsion and divisibility concepts in abelian groups to describe their structure.
Direct Sums Arithmetic
Explores the arithmetic of direct sums in group theory, discussing conditions for equality.
Introduction, Ch V: Sylow Subgroups
Explores the study of finite groups through subgroup analysis, focusing on Sylow subgroups.
Definition: Understanding Group Structures
Explores the philosophy of understanding a group through its subgroups' structure, focusing on finite groups.
Algebra: Group Actions and Direct Products
Covers group actions, conjugacy classes, centralizers, direct products, and finite abelian groups.
Groups: Definitions, Properties, and Homomorphisms
Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.
Subgroups and Cosets: Lagrange's Theorem
Explores subgroups, normal subgroups, cosets, and Lagrange's theorem in group theory, emphasizing the importance of left cosets.
Useful Lemmas for p-Groups
Covers useful lemmas for p-groups, including divisibility properties and the existence of specific elements in finite abelian groups.
Finite Abelian Groups: Classification Theorem
Presents the classification of finite abelian groups as products of cyclic groups, a fundamental result in various branches of mathematics.
Resoluble Groups: Quotients of Group
Covers the definition of solvable groups and the abelian property of group quotients.
Finitely Generated Abelian Groups
Explores finitely generated abelian groups, focusing on their structure and isomorphism theorems.
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'.
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