week 14: Isomorphism theorems and Cayley's theorem
Course Material
- week1 : Groups, Definitions and examples of groups, elementary properties of groups
- week2 : Finite and infinite Groups
- week 3: Order of a group, order of an element of a group and related results
- week 4: Subgroups and examples of subgroups, subgroup tests, subgroup generated by set
- week5: Cyclic groups, properties of cyclic groups
- week6: Classification of subgroups of cyclic groups
- week07: Cosets decomposition of a group, properties of cosets
- week08: Lagrange's theorem and its consequences. Conjugate elements and conjugacy classes
- Week 09: Mid Term Exam
- Week 10: Centralizer, Normalizer of a subset of a group. Centre of group definition and examples
- Week 11: Normal subgroups, factor groups
- week12: Permutation and permutation groups, definition and examples
- week13: Homomorphism of groups, Fundamental theorem of homomorphism
- week 14: Isomorphism theorems and Cayley's theorem
- week15: Endomorphism and automorphisms of groups
- week16: Commutator subgroups
- Week 17: External and internal direct products, definition and examples
- Week 18: Final Term Exam
- Chapters 18
- Department Mathematics
- Teacher
Ms. Asifa Ilyas
