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Group Theory: Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange's Theorem for finite groups, group homomorphism, and basic concepts of quotient groups.

Step-by-Step Plan:

Group theory can be divided into several subtopics:

Basics of sets and binary operations

Definition of groups and examples

Subgroups and cyclic groups

Cosets and Lagrange’s Theorem

Homomorphisms and Isomorphisms

Normal subgroups and quotient groups

Group actions

Sylow theorems

Direct and semidirect products

Classification of finite groups

number of generators of cyclic group of order 12

Hi BHU PET 2018, 2
Key (c)