- General InformationThis topic
- Attendance in both lectures and tutorials is compulsory and will be recorded for the purpose of engagement monitoring, in line with the School's Student Engagement Policy.
- Tutorials will start in week 1.
- The first five weeks of this module will involve going over . How much of this is review, how much is new, and how much forms a crash course in basic group theory will depend on how much group theory you have already studied. I am happy to further explain any parts of this material in the tutorials.
- There may be a lecture in week 7 – please follow the announcements.
- Useful References
Useful texts for background reading include:
- Walter Ledermann and Alan J. Weir, Introduction to Group Theory (Second Edition), Longman, 1996.
- Peter J. Cameron, Introduction to Algebra (Second Edition), Oxford University Press, 2008.
A useful reference for group actions and permutation group theory is:
- Peter J. Cameron, Permutation Groups, L.M.S. Student Texts 45, Cambridge University Press, 1999.
A very thorough and useful reference for all aspects of group theory is:
- Derek J.S. Robinson, A Course in the Theory of Groups (Second Edition), Graduate Texts in Mathematics 80, Springer, New York, 1996.
- Week 1 and Week 2
Week 1 and Week 2
The following in the notes below are NOT examinable:
- Section 1.5 (Presentations);
- from the last two paragraphs of page 12 (starting with "The group D2n has a presentation") until the end of page 15 (including the Exercise on page 15). You are still responsible, however, for the statement of the Fundamental Theorem of Abelian Groups and its application (as given in Section 2.2).
- Week 3 and week 4
Week 3 and week 4
Section 3.4 (Appendix: How many groups?) in the notes below is NOT examinable
Supplementary reading on group actions (from the blog of Tim Gowers):https://gowers.wordpress.com/2011/11/09/group-actions-ii-the-orbit-stabilizer-theorem/
- Week 5 and Week 6
Week 5 and Week 6
In the notes below, Theorem 4.4 part (b) and its proof, and the proof of the Jordan–Hölder Theorem in Appendix 5.5, are NOT examinable.
- Week 8 and Week 9
Week 8 and Week 9
On Mon, Nov 5 we have a revision lecture (instead of a usual lecture), at the usual time but not at the usual place: 10–12, Queens LG3. We have no tutorial on Friday Nov 9.
In the notes below, Section 6.3 (Digression: Minimal normal subgroups) is not examinable.
- Week 10 and Week 11
Week 10 and Week 11For the purposes of the final examination, you are only responsible to know one proof of the simplicity of An (for n greater than or equal to 5), and you are only responsible to know one proof that S6 has an outer automorphism.
A description of the outer automorphism of S6 in terms of "mystic pentagons" can be found in the notes http://math.stanford.edu/~vakil/files/sixjan2308.pdf .
- Week 12