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Saturday, October 24, 2009

M336 - Groups and Geometry

M336 starts in feb 2010. 4TMA's and 1 examination, like MS221. The M336 course covers two related topics: groups and geometry and is delivered in 16 well known OU type of books including exercises, solutions, summaries and so on. The group theory-stream consists of the following:

Axioms and examples
Generating subgroups
Cyclic groups
Group actions

Group axioms
Subgroups and cosets
Normal subgroups and quotient groups
Isomorphisms and homomorphisms
Generators and relations

Equivalent colourings
Group actions
The counting lemma
The cycle index
Polya's enumeration formula.

Direct products
Abelian groups and groups of small orders
Cyclic groups
Subgroups and quotient groups of cyclic groups
Direct products of cyclic groups

Finitely presented abelian groups
The reduction algorithm
Existence and uniqueness of torsion coefficients and rank
Finitely generated abelian groups

Finite abelian groups
Subgroups of abelian groups
Permutation groups
Conjugacy - p-groups

Sylow p-subgroups
Sylow's first and second theorems
Sylow's third theorem
Applications of the Sylow theorems
Subgroups of prime power order

Groups of order 2p
Groups of order 12
Where now?

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