Group Theory
Course Objectives: The course objective is to introduce students to the fundamental theory of
groups and their homomorphisms. Symmetric groups and symmetries in groups, Lagrange’s
theorem are also studied in depth.
Course Learning Outcomes: The course will enable the students to:
i) recognize the mathematical objects that are groups, and classify them as abelian, cyclic
and permutation groups, etc;
ii) analyze consequences of Lagrange’s theorem
iii) learn about structure preserving maps between groups and their consequences.
iv) explain the significance of the notion of cosets, normal subgroups, and factor groups.
Course Objectives: The course objective is to introduce students to the fundamental theory of
groups and their homomorphisms. Symmetric groups and symmetries in groups, Lagrange’s
theorem are also studied in depth.
Course Learning Outcomes: The course will enable the students to:
i) recognize the mathematical objects that are groups, and classify them as abelian, cyclic
and permutation groups, etc;
ii) analyze consequences of Lagrange’s theorem
iii) learn about structure preserving maps between groups and their consequences.
iv) explain the significance of the notion of cosets, normal subgroups, and factor groups.
Course Contents: Unit 1. Groups [06 lectures] 1.1 Binary Operation 1.2 Isomorphic Binary Structures 1.3 Groups Unit 2. Subgroups [06 lectures] 2.1 Subgroups 2.2 Cyclic Groups Unit 3. Permutations[12 lectures] 3.1 Groups of Permutations 3.2 Orbits 3.3 Cycles 3.4 Alternating Groups 3.5Cosets and the Theorem of Lagrange 3.6 Direct Products Unit 4.Homomorphisms and Factor Group [12 lectures] 4.1 Homomorphisms 4.2 Factor Groups 4.3 Factor Group Computations and Simple Groups