This module will be given as a reading course in the first semester. I shall teach the first half of the module; the second half will be taught by Professor Peter Cameron.

Anyone who is thinking about taking this module should see me.

The module follows on from Algebraic Structures I and is a preliminary to our level 7 algebra modules (Group Theory, Rings and Modules, and Fields and Galois Theory).

Weekly Timetable

• Friday 1100-1200 in Room 410 in the Maths building: your chance to ask me questions about what you have read.
• Friday 1500-1600 in Room 410 in the Maths building: your chance to ask questions about the exercises.

Resources

Course material will be posted here in due course. In the meantime, material from a previous version of the course can be found here.

Reading material for Week 1

You should find that most of this is revision.

• Equivalence relations.
• Review of basic group theory.
• Sections 1.18–1.20 and 3.1–3.7 of Introduction to Algebra.

Reading material for Week 2

Some of this will also be revision.

• Group homomorphisms, quotient groups and the isomorphism theorems.
• Sections 3.8–3.9 of Introduction to Algebra.

Reading material for Week 3

• Group actions.
• Section 7.1 of Introduction to Algebra.

Reading material for Week 4

• Conjugacy.
• Sections 3.10–3.14 of Introduction to Algebra.

Reading material for Week 5

• Groups of prime-power order.
• Sylow's theorems.
• Sections 7.2–7.3 of Introduction to Algebra.

Reading material for Week 6

• Simple groups.
• Composition series and soluble groups.
• Sections 7.4–7.5 of Introduction to Algebra.

See the continuation web page for the reading material for later weeks.

Links to some Theorems of the Day on algebra can be found here.

Administrative matters

My office hours for weeks 1–4 are Monday 1430–1530, Thursday 1130–1230 and Friday 1330–1430.

The syllabus and learning outcomes for this course can be found here.

Coursework will be set and marked. This will count for 10% of the final mark. The coursework box is the YELLOW box on the 2nd floor of the Mathematics building.

Coursework

• Coursework 1 for handing in by 6 October 2010.
  Here are my solutions. Please be aware that different solutions may also be correct, and may be more elegant.
• Coursework 2 for handing in by 13 October 2010.
  Here are my solutions.
• Coursework 3 for handing in by 20 October 2010.
  Here are my solutions.
• Coursework 4 for handing in by 27 October 2010.
• Coursework 5 for handing in by 3 November 2010.
• Coursework 6 for handing in by 17 November 2010.

See the continuation web page for the assignments for later weeks.

Examination material

• 2010
• 2009
• 2008
• 2007
• 2006

The examination paper in 2011 will be similar to these. You will be required to answer four questions. It will not be possible to obtain full marks by restricting yourself to either group theory or ring theory.

R. A. Bailey
Page updated 23 October 2010