The Theory of p-Groups

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