Primitive amalgams 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 algebra, 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 inprimitive permutation groups, and beyond. In this talk, we will discuss some recent progresson the central conjecture from the theory of primitive amalgams, called the Goldschmidt-Sims conjecture. Joint work with Laszlo Pyber.

group theoryrings and algebras

Audience: researchers in the topic

Al@Bicocca take-away