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Algebra seminar - Gareth Tracey

Dates:19 November 2024
Times:14:00 - 15:00
What is it:Seminar
Organiser:Department of Mathematics
Who is it for:University staff, External researchers, Current University students
Speaker:Gareth Tracey
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  • Department of Mathematics

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  • In category "Seminar"
  • In group "(Maths) Algebra"
  • By Department of Mathematics

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

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Simon Crawford

simon.crawford@manchester.ac.uk

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