MTH311 - Algebra (Group Theory)

Instructor : Dr. Anupam Kumar Singh

Schedule : The course will meet 3 hours a week. Two hours will be for lectures and one hour will be for tutorial every week.

Grading : There will be 4 exams (including mid and end semester) with weightage 25% each.

Syllabus : Definition of group and examples, Subgroups, homomorphisms, Normal subgroups, quotient groups, Lagrange's Theorem, Group Action, Cayley's Theorem, Sylow's Theorem.

Direct and Semidirect product of groups, Structure of Abelian groups.

Definition of ring and field, Finite linear group GL(n,q).

Goal of the Course : To understand what is a group and it's structure theory a bit.

References :

1. Abstract Algebra - Dummit and Foote

2. Topics in Algebra - Herstein

3. Algebra - Lang

4. Algebra - M. Artin

5. Groups and Symmetry - Armstrong

6. Groups and Representations - Alperin and Bell

7. Group Theory selected problems - B Sury

Course Information :

02/08/2011 Definition of group and examples - Assignment I

03/08/2011 Examples

05/08/2011 Tutorial

09/08/2011 Homomorphism, examples

10/08/2011 Subgroup, examples

12/08/2011 Tutorial

16/08/2011 Lagrange's Theorem - Assignment II

17/08/2011 Normalizer, Centralizer and Center

19/08/2011 Tutorial

23/08/2011 away for a workshop on Lie groups and Lie algebras at HRI, Allahabad

24/08/2011 away

26/08/2011 away

30/08/2011 Classification of Cyclic groups

31/08/2011 (extra class) Normal subgroups and Quotient groups

01/09/2011 First Test at 2PM - Question Paper

02/09/2011 tutorial

06/09/2011 Solution of exercises from test

07/09/2011 Revision of normal subgroups, quotient groups and example of Alternating group

09/09/2011 Tutorial

13/09/2011 Isometries on R^n

14/09/2011 Group of Isometries

16/09/2011 Tutorial

20/09/2011 Group Action Assignment III

21/09/2011 General Class Equation

23/09/2011 Tutorial

27/09/2011 Class Equation

28/09/2011 Application of class equation

30/09/2011 Tutorial

2-9/10/2011 mid semester break

9-12/10/2011 mid semester examination Question Paper

14/10/2011 Solution to exercises in the mid-sem exam

18/10/2011 revision of quotient groups and Isomorphism Theorem

19/10/2011 Converse of Lagarange's Theorem for Abelian groups and p-groups

21/10/2011 Tutorial

25/10/2011 Sylow's Theorem

26/10/2011 Diwali Holiday Test III

28/10/2011 Tutorial

01/11/2011 No Class

02/11/2011 Proof of Sylow's Theorem

04/11/2011 Tutorial

08/11/2011 Solution to the exercises from test III

09/11/2011 Linear groups GL_n, SL_n, PGL_n and PSL_n

11/11/2011 Tutorial

15/11/2011 The group SO(3) and SU(2)

16/11/2011 Quaternion algebra H and the covering map SU(2)-->SO(3)

18/11/2011 Tutorial

23/11/2011 End Sem Exam