Course description: The course will cover some of the topics listed below, depending on the demand of the audience.
Topics: The course attempts to give an idea of some basic methods in finite and infinite group theory. We shall cover topics like permutation actions, the Sylow-theorems , finite permutation groups, some properties of p-groups , the Schur - Zassenhaus theorem, the transfer and its applications, solvable groups, nilpotent groups, free groups. A brief introduction to character theory of finite groups.
Two sample theorems:
1. If a torsion-free group G has a cyclic subgroup of finite index, then G is cyclic.
2. If the order of G is the product of two prime powers then G is solvable.