Week 1: Binary Operations, Definitions and Examples of Groups, More Examples of Groups, Groups of Integers Modulo n under Addition and Multiplication, Finite Groups and Order of a Group.
Week 2: Elementary Properties of Groups, Problems on Elementary Properties of Groups, Definition and Examples of Subgroups, Theorems on Subgroups.
Week 3: Special Subgroups, Cyclic Group with examples Cyclic Group and its properties, Cyclic subgroups with examples and order of element, Elementary Properties of Cyclic groups.
Week 4: Permutation Groups, Symmetric Group (Sn) Order of Permutation
Week 5: Cycle Notation of Permutations, Disjoint Cycle, Even and Odd Permutation, Permutation as product Transpositions, examples and problems
Week 6: Symmetric group of Equilateral triangle, symmetric group of square, alternating group and problems, Cosets, properties of cosets.
Week 7: Some important results on cosets, Lagrange’s theorem, applications of Lagrange's theorem, Fermat and Euler’s theorems, Normal subgroups definitions and examples.
Week 8: Properties and important results on normal subgroups, some problems on normal subgroups, quotient groups with examples.
Week 9: Properties of Quotient groups with problems, Group Homomorphisms and examples, Properties of Homomorphisms and its important results
Week 10: Isomorphisms with examples and basic properties of Isomorphisms
Week 11: Fundamental theorem of homomorphism, three isomorphism theorems and problems, automorphisms
Week 12: Internal and external direct product of groups and their related results, Structure Theorem of Finite Abelian groups
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