Algebra seminar - Gareth Tracey
| Dates: | 19 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: | Gareth Tracey |
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Title: Primitive amalgams and the Goldschmidt-Sims conjecture
Abstract: A triple of finite groups (H,M,K), usually written H> M<K, is called a primitive amalgam if M is a subgroup of both H and K, and each of the following holds:
(i) Whenever A is a normal subgroup of H contained in M, we have N_K(A)=M; and (ii) whenever B is a normal subgroup of K contained in M, we have N_H(B)=M.
Primitive amalgams arise naturally in many different contexts across pure mathematics, from Tutte's study of vertex-transitive groups of automorphisms of finite,
connected, trivalent graphs; to Thompson's classification of simple N-groups; to Sims' study of point stabilizers in primitive permutation groups, and beyond. In this talk, we will discuss some recent progress on the central conjecture from the theory of primitive amalgams, called the Goldschmidt--Sims conjecture. This has, in particular, led to a shorter proof of the Sims conjecture. Joint work with László Pyber.
Speaker
Gareth Tracey
Organisation: Warwick University
Travel and Contact Information
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Frank Adams 1
Alan Turing Building
Manchester
