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Last updated:

September 23, 2023

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FREE

This course includes:

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Description

Introduction to Abstract Group Theory. Instructor: Prof. Krishna Hanumanthu, Department of Mathematics, Chennai Mathematical Institute (CMI).

This course will introduce abstract groups. We will start with definitions, basic properties and constructions and cover many important theorems in basic group theory, such as Lagrange's theorem, Cauchy's theorem and Sylow theorems. A major emphasis of the course will be to present numerous worked-out examples and problems. A part of the lecture every week will be devoted to explicit calculations. (from nptel.ac.in)

Course Curriculum

  • Lecture 01 – Motivational Examples of Groups Unlimited
  • Lecture 02 – Definition of a Group and Examples Unlimited
  • Lecture 03 – More Examples of Groups Unlimited
  • Lecture 04 – Basic Properties of Groups and Multiplication Tables Unlimited
  • Lecture 05 – Problems 1 Unlimited
  • Lecture 06 – Problems 2 Unlimited
  • Lecture 07 – Problems 3 Unlimited
  • Lecture 08 – Subgroups Unlimited
  • Lecture 09 – Types of Groups Unlimited
  • Lecture 10 – Group Homomorphisms and Examples Unlimited
  • Lecture 11 – Properties of Homomorphisms Unlimited
  • Lecture 12 – Group Isomorphisms Unlimited
  • Lecture 13 – Normal Subgroups Unlimited
  • Lecture 14 – Equivalence Relations Unlimited
  • Lecture 15 – Problems 4 Unlimited
  • Lecture 16 – Cosets and Lagrange’s Theorem Unlimited
  • Lecture 17 – S_3 Revisited Unlimited
  • Lecture 18 – Problems 5 Unlimited
  • Lecture 19 – Quotient Groups Unlimited
  • Lecture 20 – Examples of Quotient Groups Unlimited
  • Lecture 21 – First Isomorphism Theorem Unlimited
  • Lecture 22 – Examples and Second Isomorphism Theorem Unlimited
  • Lecture 23 – Third Isomorphism Theorem Unlimited
  • Lecture 24 – Cauchy’s Theorem Unlimited
  • Lecture 25 – Problems 6 Unlimited
  • Lecture 26 – Symmetric Groups I Unlimited
  • Lecture 27 – Symmetric Groups II Unlimited
  • Lecture 28 – Symmetric Groups III Unlimited
  • Lecture 29 – Symmetric Groups IV Unlimited
  • Lecture 30 – Odd and Even Permutations I Unlimited
  • Lecture 31 – Odd and Even Permutations II Unlimited
  • Lecture 32 – Alternating Groups Unlimited
  • Lecture 33 – Group Actions Unlimited
  • Lecture 34 – Examples of Group Actions Unlimited
  • Lecture 35 – Orbits and Stabilizers Unlimited
  • Lecture 36 – Counting Formula Unlimited
  • Lecture 37 – Cayley’s Theorem Unlimited
  • Lecture 38 – Problems 7 Unlimited
  • Lecture 39 – Problems 8 and Class Equation Unlimited
  • Lecture 40 – Group Actions on Subsets Unlimited
  • Lecture 41 – Sylow Theorem I Unlimited
  • Lecture 42 – Sylow Theorem II Unlimited
  • Lecture 43 – Sylow Theorem III Unlimited
  • Lecture 44 – Problems 9 Unlimited
  • Lecture 45 – Problems 10 Unlimited

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