Finite Group Theory
| Title | Finite Group Theory |
| Term | Michaelmas Term, 2010 |
| Time | Mondays, 3pm-4pm, Wednesdays 5pm-6pm |
| Location | Lecture Room 1 |
| Prerequisites | B2b Finite Group Theory |
| Lecture Notes | 99 pages, PDF |
This course is intended to develop the theory of finite groups, using B2b as a starting point. We follow a historical trail, with lectures on the 1900s, 1930s, 1960s, and 1990s.
The syllabus is (approximately) as follows.
| Lecture 1 | PSLn(q) |
| Lecture 2 | The transfer |
| Lecture 3 | p-groups and nilpotent groups |
| Lecture 4 | Frobenius groups |
| Lecture 5 | Cohomology |
| Lecture 6 | The Schur—Zassenhaus theorem |
| Lecture 7 | Hall's theorem on soluble groups |
| Lecture 8 | The Fitting subgroup |
| Lecture 9 | Nilpotence of Frobenius kernels |
| Lecture 10 | Alperin's fusion theorem |
| Lecture 11 | The focal subgroup theorem |
| Lecture 12 | The generalized Fitting subgroup |
| Lecture 13 | Saturated fusion systems |
| Lecture 14 | Normalizers and quotients |
| Lecture 15 | Alperin's fusion theorem revisited |
| Lecture 16 | Thompson's normal p-complement theorem |
Exercise sheets will be given out in Weeks 1-7 on the Monday, and due in on the Friday at noon. Examples classes will be scheduled, probably for the Monday, in the first lecture.