Algebra seminar - Scott Harper
| Dates: | 26 November 2024 |
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| Times: | 14:00 - 15:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Scott Harper |
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Title: Coverings of finite groups and derangements
Abstract: A finite group is never the union of conjugates of a proper subgroup. Equivalently, a nontrivial finite transitive permutation group always contains a derangement (a fixed-point-free permutation). This is a theorem of Jordan (1872) and it follows from a simple counting argument. I will discuss several variations on this theorem that have attracted attention over the decades, highlighting connections with number theory, graph theory and extremal combinatorics. I will then focus on the conjecture that a finite group is never the union of conjugates of two proper subgroups of the same size and discuss joint work with David Ellis towards this. Along the way, I will discuss recent work with Martin Liebeck on representations of extensions of simple groups, generalising work of Feit and Tits (1978).
Speaker
Scott Harper
Organisation: University of St Andrews
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
