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Courses in Mathematics and Statistics Level 1 Modules Level 2 Modules Level 3 Modules Level 4 Modules Level 5 Modules Honours timetable 2010/2011 Sem. 1 2010/2011 Sem. 2 2011/2012 Sem. 1 & Sem. 2 2012/2013 Sem. 1 & Sem. 2

MT5829 GROUP RINGS This course is an optional module for postgraduate courses. Undergraduates can only take it with the permission of the Director of Teaching. Aims Group rings were introduced as a tool in the representation theory of groups, and then they became objects of independent study. A group ring combines a group and a ring, so it is natural to ask how the properties of the ring and the group determine the properties of the group ring, and vice versa. The main directions of current researches in group ring theory are their ring and Lie properties, the structure of the unit group and the isomorphism problem. After a revision of necessary facts from group theory and ring theory, we will give classical results in each of these four areas; we will also point out some very recent results and open questions. Syllabus 24 lectures will cover the following topics: 1. Revision: groups and rings; 2. Definitions of group rings; basic examples; 3. Ideals and subgroups; 4. Ring and Lie properties; 5. Groups of units; 6. Isomorphism problem; 7. Modular group algebras. Tutorials will accompany these lectures with an appropriate selection of problems. Assessment Two-and-a-half Hour Examination = 100% Prerequisites MT4003 or MT4517. Availability Every year in semester 2 at 2 Lecturer Dr A B Konovalov Click here for access to past examination papers for this module. Click here to see the University Course Catalogue entry. Revised: JOC (September 2010)