### 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.

### Learning Outcomes

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

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

### Contents

1. Series in groups, normal series, normal series and its refinement
2. Composition series, equivalent composition series
3. Jordan Holder Theorem
4. Solvable groups, definition, examples and related results
5. Upper and Lower Central series, Nilpotent groups
6. Characterization of finite nilpotent groups
7. The Frattini subgroups, definition, examples and related results
8. Free groups, definition, examples and related results
9. Free Product, definition, examples and related results
10. Group algebras and representation modules

### Recommended Books

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

### Suggested Books

1. Bhattacharya P. B, Jain S. K. and Nagpaul S. R. Basic Abstract Algebra (Cambridge University Press, 2nd edition, 1994)
2. Fraleigh J. B. A First Course in Abstract Algebra, (Addison-Wesley Publishing Company, 7th edition, 2003).
3. Malik D. S., Mordeson J. N. and Sen M. K. Fundamentals of Abstract Algebra, (WCB/McGraw-Hill, 1997).
4. 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