MTH304: (Group Theory)

[Cr:4, Lc:3, Tt:1, Lb:0]

Definition of Groups, subgroups, homomorphisms, cosets, products of groups, modular arithmetic, quotient groups.
Groups via examples: Groups acting on sets, permutation groups, matrix groups, roots of unity, operations on cosets, normality, orbit stabiliser formulae, permutation representation.
Class equation, Sylow's Theorems, group of prime power order and groups of order $\leq$ 8, computations in the symmetric group.
Semi-direct products, groups of order pq.
Commutator subgroup, derived series and central series, solvable and nilpotent groups, structure of finite nilpotent groups.
Jordan Holder theorem for finite groups.
Free groups, generators and relations, examples of group presentations, free abelian groups, statement of structure theorem of finitely generated abelian groups.

Representation, group ring etc.