I’ll talk about some purposes of the construction theorem for approximate teams proved some years in the past by Hurshovski and Breuillard-Inexperienced-Tao. We describe the construction of finite teams with very massive diameter (bigger than an influence of the scale of the group). Particularly we get hold of a common higher certain on the diameter of Cayley graphs of finite easy teams, which is unbiased of CFSG. Utilizing the construction of nilprogressions, we present that these teams (which we name virtually flat) are exactly the teams of average development launched by Diaconis and Saloff-Coste within the 90’s in reference to mixing time estimates for random walks (joint work with Matt Tointon).
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