Topics in Group Theory

This website is for the 4th year course at the Universidad de Costa Rica starting Monday 10th March, 2014.

Practical matters

  • Lectures: There are two lectures per week (Monday, 15:00 – 17:50 and Thursday, 16:00 – 17:50) in Room 400. There will be 80 hours of lectures in total.
  • Lecture notes: These will be put online on Thursday afternoon each week.
  • Office hours: Mondays 2 – 3pm and Thursdays 2 – 4pm.
  • Assessment: There will be two exams, each counting 40% of the total mark. The remaining 20% of the mark will be for exercises.
    • The first exam has happened. Answers are here.
    • The second exam has happened. Answers are here.
  • La carta al estudiante (in Spanish).

Lecture notes

Exercises

I will provide full answers for the first set, thereafter answers will only be provided on request.

Background reading
No one text covers all of the material in this course. Principal texts are as follows:

  • John D. Dixon and Brian Mortimer, Permutation groups, Graduate Texts in Mathematics, vol. 163, Springer-Verlag, New York, 1996.
  • Peter Cameron’s notes on Classical Groups;
  • Peter Cameron’s notes on Projective and polar spaces (First edition published as QMW Maths Notes 13 in 1991).

Additional texts of interest:

  • Harald Simmons, An introduction to category theory. (I drew on a very small part of these notes when I wrote the chapter on category theory.)
  • Jean Dieudonne, La geometrie des groupes classiques. This is a classic, in French.
  • Peter Kleidman and Martin Liebeck, The subgroup structure of the finite classical groups. This proves a refined version of Aschbacher’s theorem on the subgroup structure of the finite classical groups. It also contains a wealth of other information on these groups (and other almost simple groups).
  • Donald Taylor, The geometry of the classical groups. This covers all the material in the second half of this course plus a fair bit more.
  • Helmut Wielandt, Finite permutation groups. Another classic giving a good sense of the major themes in the development of the theory of finite permutation groups.
  • Robert Wilson, Finite simple groups. Related lecture notes are online.
  • Joanna Fawcett, The O’Nan-Scott theorem for finite primitive permutation groups. A very nice Masters thesis giving a self-contained proof of the O’Nan-Scott theorem.

I have e-copies of most of the texts listed above and can provide them on request.

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  1. Pingback: Crecimiento en grupos y otras estructuras | Nick Gill

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