Finite classical groups

This is the webpage for my course with the London Taught Course Centre. Practical matters:

• Lectures: There are 5 lectures, given every Monday from 13th January until 10th February 2025, 3:10pm – 5:10pm at De Morgan house in London.
• Lecture notes: These will be put online the morning after the lecture is given. Each lecture contains many exercises which students are encouraged to attempt. Answers to starred exercises will be put online after one week.
• Exam: Information will be provided in due course.

Course material follows.

• Useful reading:
  • Course description, including a list of background texts;
  • Peter Cameron’s notes on Classical Groups;
  • Peter Cameron’s notes on Projective and polar spaces.
• Lecture notes:
  • Lecture 0 on Group theory background (this was not covered in class);
  • Lecture 1 on Permutation Groups and Fields and Vector Spaces;
  • Lecture 2 on Projective space and Linear groups;
  • Lecture 3 on Forms and polar spaces and Isometries and Witt’s Lemma;
  • Lecture 4 in which we finish off Isometries and Witt’s Lemma, and then cover Polar spaces and Symplectic groups;
  • Lecture 5 on Unitary groups and Orthogonal groups.
• Exercises and discussion class:
  • Exercises 0 (including solutions);
  • Exercises 1 (including solutions);
  • Exercises 2 (including solutions);
  • Exercises 3 (including solutions);
  • Exercises 4 (including solutions);
  • Exercises 5 (including solutions).