Estb. 1882

University of the Punjab

MATH-302 Group Theory-I

Groups  Definition and examples of groups
 Abelian group
 Subgroups lattice, Lagrange’s theorem
 Relation between groups
 Cyclic groups
 Groups and symmetries, Cayley’s theorem Complexes in Groups  Complexes and coset decomposition of groups
 Centre of a group
 Normalizer in a group
 Centralizer in a group
 Conjugacy classes and congruence relation in a group
 Double cosets
Normal Subgroups  Normal subgroups
 Proper and improper normal subgroups
 Factor groups
 Fundamental theorem of homomorphism
 Automorphism group of a group
 Commutator subgroups of a group Sylow Theorems  Cauchy’s theorem for Abelian and non-Abelian group
 Sylow theorems
Credit hours/ Marks:- 3

Reference Books

Download Course-Outline