Elementary Properties of Groups
Course Material
- Definition of a group and examples
- Elementary Properties of Groups
- Symmetries of a Square, The Dihedral Groups
- Subgroup: Terminology and Notation, Subgroup Tests
- Examples of Subgroups
- Cyclic Groups :Definition and examples
- Properties of Cyclic Groups
- Classification of Subgroups of Cyclic Groups
- Cosets and Lagrange’s theorem
- Mid Term Exam
- Normalizer,Centralizer, Center of a group
- Equivalence relation in a group, Conjugacy classes
- Equivalence relation in a group, Conjugacy classes
- Conjugacy classes, Normal subgroups, Quotient group
- Homomorphism, isomorphism and automorphism
- kernel and image of homomorphism, isomorphism theorems
- Permutation groups, Cyclic decomposition of a permutation group, Cayley’s theorem, direct product of two groups and examples
- Final Term Exam
- Chapters 18
- Department Mathematics(SCB)
- Teacher
Ms. Ammara Nazar
