**Discription**

This course is the continuation of the course "Advanced Group Theory-I" and covers the advanced topics in group theory such as solvable groups, nilpotent groups, and linear groups.

**Pre-Requisite**

Advance Group Theory-I

**Learning Outcomes**

On successful completion of this course students will be able to:

- define solvable groups, nilpotent groups
- derive upper and lower central series, derived series and representation of linear groups
- reason mathematically, to write simple proofs, and can judge when an attempted proof in group theory is correct/complete or is not.
- have a chance to reflect on doing mathematics, solving problems and on our role and progress as mathematicians.

**Contents**

- Series in groups, normal series, normal series and its refinement
- Composition series, equivalent composition series
- Jordan Holder Theorem
- Solvable groups, definition, examples and related results
- Upper and Lower Central series, Nilpotent groups
- Characterization of finite nilpotent groups
- The Frattini subgroups, definition, examples and related results
- Free groups, definition, examples and related results
- Free Product, definition, examples and related results
- Group algebras and representation modules

**Recommended Books **

- Rotman J. J.,
*An Introduction to the theory of groups*, (Springer; 4th edition, 1999).
- Shah S
*. *K., Shankar A. G., *Group Theory*, (Dorling Kindersley 2013).

**Suggested Books **

- Bhattacharya P. B, Jain S. K. and Nagpaul S. R.
* Basic Abstract Algebra* (Cambridge University Press, 2nd edition, 1994)
- Fraleigh J. B. A
* First Course in Abstract Algebra**,* (Addison-Wesley Publishing Company, 7th edition, 2003).
- Malik D. S., Mordeson J. N. and Sen M. K.
*Fundamentals of Abstract Algebra*, (WCB/McGraw-Hill, 1997).
- Rose J.,
*A Course on Group Theory*, (Dover Publications; Revised edition 2012).

**Assessment Criteria**

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam: 30

Final-Term Exam: 50

**Key Dates and Time of Class Meeting**

Monday 02:00 PM-03:30 PM (Ex-PPP)

Tuesday 11:00 AM-12:00 PM (Main Campus)

Wednesday 11:00 AM-12:00 PM (Ex-PPP)

Thursday 11:00 AM-12:00 PM (Main Campus)

Commencement of Classes January 13, 2020

Mid Term Examination March 09-13, 2020

Final Term Examination May 04-08, 2020

Declaration of Result May 19, 2020