Pure Colloquium Seminar - Tim Burness Seminar
- Time:
- 15:00 - 16:00
- Date:
- 10 February 2017
- Venue:
- Building 54, Mathematical Sciences Building, Room 10037 - Lecture Theatre 10B, University of Southampton, Highfield, Southampton, SO17 1BJ
For more information regarding this seminar, please telephone Dr Jan Spakula on 023 8059 3137 or email Jan.Spakula@southampton.ac.uk .
Event details
Abstract: It is well known that every finite simple group can be generated by two elements and this leads to a wide range of problems that have been the focus of intensive research in recent years, such as random generation, (2,3)-generation and so on. In this talk I will report on recent joint work with Martin Liebeck and Aner Shalev concerning similar problems for subgroups of (almost) simple groups. We prove that every maximal subgroup of a simple group can be generated by four elements (this is best possible) and we show that the problem of determining a bound on the number of generators for second maximal subgroups depends on a formidable open problem in Number Theory. Time permitting, we will also discuss some related results on random generation and subgroup growth.
Speaker information
Dr Tim Burness , University of Bristol. His main area of research is in group theory. He is interested in simple groups, both finite and algebraic, with a particular focus on subgroup structure, conjugacy classes and representation theory. He is also interested in permutation groups and related combinatorics, and in the application of probabilistic and computational methods.