Introduction to Abstract Group Theory

By Prof. Krishna Hanumanthu   |   Chennai Mathematical Institute
Learners enrolled: 1286
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. 

INTENDED AUDIENCE: BSc, MSc students studying mathematics

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

Course Status : Completed
Course Type : Core
Duration : 8 weeks
Category :
  • Mathematics
  • Algebra
  • Foundations of Mathematics
Credit Points : 2
Level : Undergraduate/Postgraduate
Start Date : 25 Jul 2022
End Date : 16 Sep 2022
Enrollment Ends : 08 Aug 2022
Exam Date : 25 Sep 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

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

Books and references


Instructor bio

Prof. Krishna Hanumanthu

Chennai Mathematical Institute
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. 

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 25 September 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
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. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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