University of Birmingham > Talks@bham > Groups St Andrews 2017 > The diameter of the symmetric group: ideas and tools

The diameter of the symmetric group: ideas and tools

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Given a finite group G and a set A of generators, the diameter diam(Γ(G,A)) of the Cayley graph Γ(G,A) is the smallest ℓ such that every element of G can be expressed as a word of length at most ℓ in AA-1. We are concerned with bounding diam(G) := maxA diam(Γ(G,A)).

It has long been conjectured that the diameter of the symmetric group of degree n is polynomially bounded in n. In 2011, Helfgott and Seress gave a quasipolynomial bound (exp((log n)(4+ε))). We will discuss a recent, much simplified version of the proof, emphasising the links in commons with previous work on growth in linear algebraic groups.

This talk is part of the Groups St Andrews 2017 series.

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