Courses » Introduction to Abstract Group Theory

Introduction to Abstract Group Theory


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.

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Weekly Assignments and Discussion Forum can be accessed ONLY by enrolling here

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Note: Content is Free!

All content including discussion forum and assignments, is free

Final Exam (in-person, invigilated, currently conducted in India) is mandatory for Certification and has INR Rs. 1100 as exam fee.

BSc, MSc students studying mathematics


UG/PG: UG and PG

PREREQUISITES: Any BSc student who is familiar with high school mathematics can take this coursel



Krishna Hanumanthu is an associate professor of mathematics at Chennai Mathematical Institute (CMI). He studied BSc and MSc in CMI during 1998-2003 and did his PhD in mathematics at University of Missouri during 2003-2008. He joined CMI as a faculty member in 2011 after working for 3 years at University of Kansas. His main areas of research are algebraic geometry and commutative algebra. He has been teaching for almost 15 years and taught introductory courses on abstract algebra (including group theory) many times.


Week 1  :  Motivation, definition, examples and basic properties
Week 2  :   Subgroups, subgroups of integers, homomorphisms
Week 3  : Quotient groups, isomorphism theorems
Week 4  :  Group operations, counting formula
Week 5  :  Symmetric groups
Week 6  :  Operations of a group on itself, class equation
Week 7  :  Sylow theorems I
Week 8  :  Sylow theorems II
  • The exam is optional for a fee.
  • Date and Time of Exam: October 28, 2018 (Sunday)
  • Time of Exams: Morning session 9am to 12 noon; Afternoon session: 2pm to 5pm.
  • Exam for this Course will be available in both morning & afternoon sessions.
  • Registration url: Announcements will be made when the registration form is open for registrations.
  • The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published.


  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 6 out of 8 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IITMadras.It will be e-verifiable at http://nptel.ac.in/noc/