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