NOTE: Attempt any FIVE questions selecting at least TWO questions from each section.

Section-I (4/9)

The Orbit Stablizer Theorem

•    Stablizer, Orbit, A group with p2 elements

•    Simplicity of An, n ≥ 5

•    Classification of Groups with at most 8 elements

Sylow Theorems

•    Sylow theorems (with proofs)

•    Applications of Sylow Theory

Products in Groups

•    Direct Products

•    Classification of Finite Abelian Groups

•    Characteristic and fully invariant subgroups

•    Normal products of groups

•    Holomorph of a group



Section-II (5/9)

Series in Groups

•    Series in groups

•    Zassenhaus lemma

•    Normal series and their refinements

•    Composition series

•    The Jordan Holder Theorem

Solvable Groups

•    Solvable groups, Definition and examples

•    Theorems on solvable groups

Nilpotent Groups

•    Characterisation of finite nilpotent groups

•    Frattini subgroups

Extensions

•    Central extensions

•    Cyclic extensions

•    Groups with at most 31 elements

Linear Groups

•    Linear groups, types of linear groups

•    Representation of linear groups

•    The projective special linear groups