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Group Theory I

By Dr. Ragi Puthan Veettil   |   Pazhassi Raja NSS college, Mattanur
Learners enrolled: 113
The course “Group Theory I” is proposed for B.Sc. (Hons) Mathematics.  The course starts with the overview of binary operations on a set, the definition of groups, cyclic groups, groups of symmetries of  a square, the external direct product of groups, normal subgroups, homomorphism, the kernel of homomorphisms, Isomorphisms, and the three isomorphism theorems
Summary
Course Status : Upcoming
Course Type : Core
Duration : 16 weeks
Category :
  • Mathematics
Credit Points : 5
Level : Undergraduate
Start Date : 01 Jul 2024
End Date : 31 Oct 2024
Enrollment Ends : 31 Aug 2024
Exam Date : 14 Dec 2024 IST
Exam Shift :

Shift 2

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.


Page Visits



Course layout

Weeks Weekly Lecture Topics (Module Titles)

1 Day 1 Module 1: Binary Operations
Day 2 Module 2: Introduction to Groups
Day 3 Module 3: More Examples to Groups
Day 4 Assignment
Day 5 Quiz

2 Day 1 Module 4 : Elementary properties of Groups
Day 2 Module 5 : Subgroups
Day 3 Module 6 : Cyclic Groups
Day 4 Assignment
Day 5 Quiz

3 Day 1 Module 7 : Properties of Cyclic Groups
Day 2 Module 8 : Classification of Subgroups of Cyclic Groups
Day 3 Module 9 : Problems on subgroups of cyclic group
Day 4 Assignment
Day 5 Quiz

4 Day 1 Module 10 : Order of an element
Day 2 Module 11 : : Permutation Groups
Day 3 Module 12 Symmetric Group S_n
Day 4 Assignment
Day 5 Quiz

5 Day 1 Module 13 : Orbits and Cycles
Day 2 Module 14 : On Cyclic Permutations
Day 3 Module 15 : Permutation as  product of Transpositions
Day 4 Assignment
Day 5 Quiz

6 Day 1 Module 16 : Alternating Groups A_n
Day 2 Module 17 : Generating Sets of S-n and A_n
Day 3 Module 18 : Conjugate Elements,Conjugacy Class
Day 4 Assignment
Day 5 Quiz

7 Day 1 Module 19 : Conjugacy in S_n
Day 2 Module 20 : The Dihedral Group
Day 3 Module 21 : Quaternion Group
Day 4 Assignment
Day 5 Quiz

8 Day 1 Module 22 : Some Problems of Permutation Group
Day 2 Module 23: Cosets
Day 3 Module 24 :  Lagrange's Theorem
Day 4 Assignment
Day 5 Quiz

9 Day 1 Module 25 : Fermat's  Theorem
Day 2 Module 26 : External Direct Product -Part I
Day 3 Module 27: External Direct Product -Part II
Day 4 Assignment
Day 5 Quiz

10 Day 1 Module 28 : Group Homomorphism -Part I
Day 2 Module 29 : Properties of Homomorphism
Day 3 Module 30 : Group Homomorphism -Part II
Day 4 Assignment
Day 5 Quiz

11 Day 1 Module 31 : Normal Subgroups
Day 2 Module 32 : Kernel of a Homomorphism-Part I
Day 3 Module 33: Kernel of a Homomorphism-Part II
Day 4 Assignment
Day 5 Quiz

12 Day 1 Module 34 : Index of  a Subgroup
Day 2 Module 35 : Factor Groups-Part I
Day 3 Module 36 : Factor Groups-Part II
Day 4 Assignment
Day 5 Quiz

13 Day 1 Module 37 : Examples of Normal Subgroups
Day 2 Module 38 : Problems in Cosets and Factor Groups
Day 3 Module 39 : Cauchy's Theorem
Day 4 Assignment
Day 5 Quiz

 14 Day 1 Module 40 : Group Isomorphism
Day 2 Module 41 : Properties of Isomorphism
Day 3 Module 42 : The First Isomorphism Theorem
Day 4 Assignment
Day 5 Quiz

 15 Day 1 Module 43 : Prerequisites for Second Isomorphism Theorem
Day 2 Module 44 : Second Isomorphism Theorem
Day 3 Module 45 : Third Isomorphism Theorem
Day 4 Assignment
Day 5 Quiz

 16 Day 1 Module 46 : Cayley's Theorem
Day 2 Module 47 : Product of Subgroups
Day 3 Module 48 : Center of a Group
Day 4 Assignment
Day 5 Quiz

 17 Day 1 Module 49 : Centralizer of an element
Day 2 Module 50 : Normalizer of a subgroup
Day 3 Module 51: Commutator Subgroup
Day 4 Assignment
Day 5 Quiz

Books and references

1.  John B Fraleigh, A first Course in Abstract Algebra,7th edition,Pearson,2002.
2.  Joseph A Gallian, Contemporary Abstract Algebra,4th edition,Narosa Publishing House,New Delhi,1999.

Instructor bio

Dr. Ragi Puthan Veettil

Pazhassi Raja NSS college, Mattanur
12 years of experience in teaching both Undergraduate and post-graduate level Mathematics.
Awarded M.Phil. from the Kerala University in 2011  Completed a Minor Research Project funded by UGC during 2015-2017.
Awarded PhD from Kannur University in Graph Theory, in 2022.

Course certificate

30 Marks will be allocated for Internal Assessment and 70 Marks will be allocated for end term proctored examination
Securing 40% in both separately is mandatory to pass the course and get Credit Certificate.


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