The Theory of p-Groups
Title | The Theory of p-Groups |
Term | Hilary Term, 2008 |
Time | Fridays, 2pm-4pm |
Location | Seminar Room 2 |
Prerequisites | B2b Finite Group Theory |
Lecture Notes | 48 pages, PDF |
This course is intended to develop the theory of finite p-groups from where it is normally left by undergraduate group theory courses (results like the centre is non-trivial) to some of the more interesting results at the foundations of the subject. No attempt is made at comprehensiveness, and such historically important topics such as commutator collection, regular p-groups, the associated Lie ring, and so on, are omitted.
The syllabus is as follows.
Week 1 | Introduction and motivation, recap theory of p-groups |
Week 2 | Commutators and automorphisms |
Week 3 | Extraspecial p-groups |
Week 4 | Automorphisms of extraspecial groups, 2-groups of maximal class |
Week 5 | 2-groups of maximal class, groups of p-rank 1 |
Week 6 | Fixed-point-free automorphisms |
Week 7 | Thompson's Critical Subgroup Theorem |
Week 8 | Fusion of p-subgroups in finite groups |