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MTH633 : Group Theory

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Course Info
Course Category	Mathematics
Course Level	Undergraduate
Credit Hours	3
Pre-requisites	N/A
Instructor	Dr. Imran Ahmed Ph.D. Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

Course Contents
Properties of real numbers Properties of complex numbers Bijective maps Inversion Theorem Isomorphic binary structures Groups Abelian Groups Finite Groups Subgroups Examples on subgroup test Cyclic Groups Elementary properties of Cyclic groups Fundamental Theorem of Cyclic Group Permutation Groups Theorem on permutation groups Orbits Cycle Decomposition Direct product Cosets Partition of group Lagrange's Theorem Homomorphism of Groups Normal Subgroups Morphism Theorem for groups Factor group Normal groups and Inner Automorphism Simple Group Generating set Commutator subgroup Automorphisms Group Action on set Stablizer Conjugacy and G-sets Isomorphism Theorem Sylow Theorems First Sylow Theorems Second Sylow Theorems Third Sylow Theorems