Details of MA3207 (Spring 2026)
| Level: 3 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3207 | Groups and Modules | Arjun Paul |
| Syllabus |
|---|
| Syllabus:
Group theory: Review of group actions, conjugacy classes, orbits and stabilizers, class equations. Syllows theorems and their applications. Classification of finite abelian groups, simple groups, simplicity of . Solvable groups, nilpotent groups, composition series, Jordan-Holder theorem. Modules: Modules and module homomorphisms, submodule and quotient modules, operations on submodules, direct sum and product, finitely generated modules, classification of finitely generated modules over PIDs, exact sequences of modules, tensor product of modules, canonical forms (if time permits). |
| Prerequisite |
|---|
| Basic algebra (MA2205), Ring theory (MA3102). |
| References |
|---|
| References:
1. Artin, M., Algebra, Prentice-Hall. 2. Dummit, D.S. and Foote, R.M., Abstract Algebra, Wiley. 3. Fraleigh, J.B., A First Course in Abstract Algebra, Narosa Publishers. 4. Gopalakrishnan, N.S., University Algebra, New Age International. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | MP ( Mathematical Sciences ) | 2 | Core |
| 4 | MP | 4 | Not Allowed |
| 5 | MR | 2 | Not Allowed |
| 6 | MR | 4 | Not Allowed |
| 7 | MS | 10 | Elective |
| 8 | MS | 4 | Not Allowed |
| 9 | MS ( Mathematical Sciences ) | 6 | Core |
| 10 | MS | 8 | Elective |
| 11 | RS | 1 | Elective |
| 12 | RS | 2 | Elective |