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 …

This is a survey of methods developed in the last few years to prove results on growth in non-
commutative groups. These techniques have their roots in both additive combinatorics and …

Expansion in finite simple groups of Lie type Page 1 DOI 10.4171/JEMS/533 J. Eur. Math. Soc.
17, 1367–1434 c European Mathematical Society 2015 Emmanuel Breuillard · Ben Green …

Let Ω be a set of cardinality n, G a permutation group on Ω, and f: Ω→ Ω a map which is not a
permutation. We say that G synchronizes f if the semigroup< G, f> contains a constant map …

Let G=< S> be a group, and let Γ be its Cayley graph. Computing the diameter of Γ is a
computationally hard problem which comes up in several contexts. Thus, it is useful to be …

Let be a set of cardinality, be a permutation group on and be a map that is not a permutation.
We say that synchronizes if the transformation semigroup contains a constant map, and that …

A well-known conjecture of Babai states that if G is a finite simple group and X is a
generating set of G, then the diameter of the Cayley graph Cay (G, X) is bounded above by …

Let G be a finite classical group generated by transvections, ie, one of SL n (q), SU n (q), Sp
2 n (q), or O 2 n±(q)(q even), and let X be a generating set for G containing at least one …

Let G be a finite group with a generating set A. By the (symmetric) diameter of G with respect
to A we mean the maximum over g in G of the length of the shortest word in (A union A …

Consider G as a finite group with a generating set A. We define the (symmetric) diameter of
G with respect to A as the maximum length of the shortest word in (A∪ A-1) A expressing g …