Mathematics
MA344: Groups II (5 ECTS)
The course covers monoids and groups and their actions. Topics covered include finite state machines, orbits and stabilizers, applications in combinatorics (e.g. vertex colorings), Sylow theory, finite simple groups.
Taught in Semester(s) 2. Examined in Semester(s) 2.
Workload: 106 hours (24 Lecture hours, 12 Tutorial hours, 70 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Define monoid actions; state and prove fundamental theorems about them.
- Determine regular languages for finite automata.
- Use orbit-stabilizer theory to compute automorphism groups of graphs.
- State and prove Sylow's theorems.
- Prove there is no finite non-abelian simple group of order less than 60.
Indicative Content
The course covers monoids and groups and their actions. Topics covered include finite state machines, orbits and stabilizers, applications in combinatorics (e.g. vertex colorings), Sylow theory, finite simple groups.
Module Resources
- M. Aschbacher, Finite group theory, Cambridge University Press
- W. Burnside, Theory of groups of finite order, 2nd ed., Cambridge University Press
- A. Kerber, Applied finite group actions, Springer
- W. R. Scott, Group theory, Prentice-Hall
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